UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE 13G

UNDER THE SECURITIES EXCHANGE ACT OF 1934
(Amendment No. )*

Trevi Therapeutics, Inc.

(Name of Issuer)

Common Stock, $0.001 par value

(Title of Class of Securities)

89532M101

(CUSIP Number)

April 11, 2022

(Date of Event Which Requires Filing of This Statement)

Check the appropriate box to designate the rule pursuant to which this Schedule is filed:

¨ Rule 13d-1(b)

x Rule 13d-1(c)

¨ Rule 13d-1(d)

* The remainder of this cover page shall be filled out for a reporting person’s initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

CUSIP No. 89532M101 Page 2 of 17

1.	Name of reporting persons Venrock Healthcare Capital Partners II, L.P.
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization Delaware

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) PN

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 3 of 17

1.	Name of reporting persons VHCP Co-Investment Holdings II, LLC
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization Delaware

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) OO

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 4 of 17

1.	Name of reporting persons Venrock Healthcare Capital Partners III, L.P.
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization Delaware

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) PN

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 5 of 17

1.	Name of reporting persons VHCP Co-Investment Holdings III, LLC
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization Delaware

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) OO

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 6 of 17

1.	Name of reporting persons Venrock Healthcare Capital Partners EG, L.P.
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization Delaware

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) PN

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 7 of 17

1.	Name of reporting persons VHCP Management II, LLC
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization Delaware

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) OO

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 8 of 17

1.	Name of reporting persons VHCP Management III, LLC
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization Delaware

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) OO

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 9 of 17

1.	Name of reporting persons VHCP Management EG, LLC
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization Delaware

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) OO

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 10 of 17

1.	Name of Reporting Persons Shah, Nimish
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization United States

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) IN

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 11 of 17

1.	Name of Reporting Persons Koh, Bong
2.	Check the Appropriate Box if a Member of a Group (See Instructions) (a) x1 (b) ¨
3.	SEC USE ONLY
4.	Citizenship or Place of Organization United States

Number of Shares Beneficially Owned by Each Reporting Person With:	5.	Sole Voting Power 0
	6.	Shared Voting Power 3,668,3342
	7.	Sole Dispositive Power 0
	8.	Shared Dispositive Power 3,668,3342

9.	Aggregate Amount Beneficially Owned by Each Reporting Person 3,668,3342
10.	Check if the Aggregate Amount in Row (9) Excludes Certain Shares (See Instructions) ¨
11.	Percent of Class Represented by Amount in Row (9) 9.99%3
12.	Type of Reporting Person (See Instructions) IN

1 Venrock Healthcare Capital Partners II, L.P., VHCP Co-Investment Holdings II, LLC, Venrock Healthcare Capital Partners III, L.P., VHCP Co-Investment Holdings III, LLC, Venrock Healthcare Capital Partners EG, L.P., VHCP Management II, LLC, VHCP Management III, LLC, VHCP Management EG, LLC, Nimish Shah and Bong Koh are members of a group for the purposes of this Schedule 13G.

2 Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.

3 This percentage is calculated based upon (i) 30,805,804 shares outstanding as of March 17, 2022, as reported in the Issuer’s Annual Report on Form 10-K filed with the Securities and Exchange Commission on March 17, 2022, plus (ii) 4,580,526 shares issued on April 11, 2022 as part of a private placement, plus (iii) 1,333,727 shares issuable upon the exercise of the Warrants described in Footnote 2 above.

CUSIP No. 89532M101 Page 12 of 17

Introductory Note: This Schedule 13G is filed on behalf of Venrock Healthcare Capital Partners II, L.P., a limited partnership organized under the laws of the State of Delaware (“VHCP II LP”), VHCP Co-Investment Holdings II, LLC, a limited liability company organized under the laws of the State of Delaware (“VHCP Co-Investment II”), Venrock Healthcare Capital Partners III, L.P., a limited partnership organized under the laws of the State of Delaware (“VHCP III LP”), VHCP Co-Investment Holdings III, LLC, a limited liability company organized under the laws of the State of Delaware (“VHCP Co-Investment III”), Venrock Healthcare Capital Partners EG, L.P., a limited partnership organized under the laws of the State of Delaware (“VHCP EG”), VHCP Management II, LLC, a limited liability company organized under the laws of the State of Delaware (“VHCP Management II”), VHCP Management III, LLC, a limited liability company organized under the laws of the State of Delaware (“VHCP Management III”), VHCP Management EG, LLC, a limited liability company organized under the laws of the State of Delaware (“VHCP Management EG” and collectively with VHCP II LP, VHCP Co-Investment II, VHCP III LP, VHCP Co-Investment III, VHCP EG, VHCP Management II and VHCP Management III, the “Venrock Entities”), Nimish Shah (“Shah”) and Bong Koh (“Koh”) in respect of Common Stock of Trevi Therapeutics, Inc.

Item 1.

(a) Name of Issuer

Trevi Therapeutics, Inc.

(b) Address of Issuer’s Principal Executive Offices

195 Church Street, 14^th Floor

New Haven, Connecticut 06510

Item 2.

(a) Name of Person Filing

Venrock Healthcare Capital Partners II, L.P.

VHCP Co-Investment Holdings II, LLC

Venrock Healthcare Capital Partners III, L.P.

VHCP Co-Investment Holdings III, LLC

Venrock Healthcare Capital Partners EG, L.P.

VHCP Management II, LLC

VHCP Management III, LLC

VHCP Management EG, LLC

Nimish Shah

Bong Koh

(b) Address of Principal Business Office or, if none, Residence

New York Office:	Palo Alto Office:
7 Bryant Park	3340 Hillview Avenue
23rd Floor	Palo Alto, CA 94304
New York, NY 10018

(c) Citizenship

All of the Venrock Entities were organized in Delaware. The individuals are both United States citizens.

(d) Title of Class of Securities

Common Stock, par value $0.001 per share

(e) CUSIP Number

89532M101

CUSIP No. 89532M101 Page 13 of 17

Item 3. If this statement is filed pursuant to §§240.13d-1(b), or 240.13d-2(b) or (c), check whether the person filing is a:

Not applicable

Item 4. Ownership

(a) Amount Beneficially Owned as of April 21, 2022:

Venrock Healthcare Capital Partners II, L.P.	3,668,334	(1)
VHCP Co-Investment Holdings II, LLC	3,668,334	(1)
Venrock Healthcare Capital Partners III, L.P.	3,668,334	(1)
VHCP Co-Investment Holdings III, LLC	3,668,334	(1)
Venrock Healthcare Capital Partners EG, L.P.	3,668,334	(1)
VHCP Management II, LLC	3,668,334	(1)
VHCP Management III, LLC	3,668,334	(1)
VHCP Management EG, LLC	3,668,334	(1)
Nimish Shah	3,668,334	(1)
Bong Koh	3,668,334	(1)

(b) Percent of Class as of April 21, 2022:

Venrock Healthcare Capital Partners II, L.P.	9.99	%
VHCP Co-Investment Holdings II, LLC	9.99	%
Venrock Healthcare Capital Partners III, L.P.	9.99	%
VHCP Co-Investment Holdings III, LLC	9.99	%
Venrock Healthcare Capital Partners EG, L.P.	9.99	%
VHCP Management II, LLC	9.99	%
VHCP Management III, LLC	9.99	%
VHCP Management EG, LLC	9.99	%
Nimish Shah	9.99	%
Bong Koh	9.99	%

(c) Number of shares as to which the person has, as of April 21, 2022:

(i) Sole power to vote or to direct the vote

Venrock Healthcare Capital Partners II, L.P.	0
VHCP Co-Investment Holdings II, LLC	0
Venrock Healthcare Capital Partners III, L.P.	0
VHCP Co-Investment Holdings III, LLC	0
Venrock Healthcare Capital Partners EG, L.P.	0
VHCP Management II, LLC	0
VHCP Management III, LLC	0
VHCP Management EG, LLC	0
Nimish Shah	0
Bong Koh	0

CUSIP No. 89532M101 Page 14 of 17

(ii) Shared power to vote or to direct the vote

Venrock Healthcare Capital Partners II, L.P.	3,668,334	(1)
VHCP Co-Investment Holdings II, LLC	3,668,334	(1)
Venrock Healthcare Capital Partners III, L.P.	3,668,334	(1)
VHCP Co-Investment Holdings III, LLC	3,668,334	(1)
Venrock Healthcare Capital Partners EG, L.P.	3,668,334	(1)
VHCP Management II, LLC	3,668,334	(1)
VHCP Management III, LLC	3,668,334	(1)
VHCP Management EG, LLC	3,668,334	(1)
Nimish Shah	3,668,334	(1)
Bong Koh	3,668,334	(1)

(iii) Sole power to dispose or to direct the disposition of

Venrock Healthcare Capital Partners II, L.P.	0
VHCP Co-Investment Holdings II, LLC	0
Venrock Healthcare Capital Partners III, L.P.	0
VHCP Co-Investment Holdings III, LLC	0
Venrock Healthcare Capital Partners EG, L.P.	0
VHCP Management II, LLC	0
VHCP Management III, LLC	0
VHCP Management EG, LLC	0
Nimish Shah	0
Bong Koh	0

(iv) Shared power to dispose or to direct the disposition of

Venrock Healthcare Capital Partners II, L.P.	3,668,334	(1)
VHCP Co-Investment Holdings II, LLC	3,668,334	(1)
Venrock Healthcare Capital Partners III, L.P.	3,668,334	(1)
VHCP Co-Investment Holdings III, LLC	3,668,334	(1)
Venrock Healthcare Capital Partners EG, L.P.	3,668,334	(1)
VHCP Management II, LLC	3,668,334	(1)
VHCP Management III, LLC	3,668,334	(1)
VHCP Management EG, LLC	3,668,334	(1)
Nimish Shah	3,668,334	(1)
Bong Koh	3,668,334	(1)

CUSIP No. 89532M101 Page 15 of 17

(1) Consists of (i) 375,639 shares and 214,597 shares issuable upon the exercise of immediately exercisable pre-funded warrants (“Warrants”) held by Venrock Healthcare Capital Partners II, L.P., (ii) 152,212 shares and 86,959 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings II, LLC, (iii) 811,976 shares and 463,870 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners III, L.P., (iv) 81,244 shares and 46,414 shares issuable upon the exercise of Warrants held by VHCP Co-Investment Holdings III, LLC and (v) 913,536 shares and 521,887 shares issuable upon the exercise of Warrants held by Venrock Healthcare Capital Partners EG, L.P. The share numbers in the preceding sentence represent the maximum number of shares of common stock issuable upon exercise of the Warrants held by the Reporting Persons as a result of the beneficial ownership provision described in the following sentence. Under the terms of the Warrants, the Issuer may not effect the exercise of any such Warrant, and a holder will not be entitled to exercise any portion of such Warrant, if, upon giving effect to such exercise, the aggregate number of shares of common stock beneficially owned by the holder (together with its affiliates and other attribution parties) would exceed 9.99% of the number of shares of common stock outstanding immediately after giving effect to the exercise.   VHCP Management II, LLC is the general partner of Venrock Healthcare Capital Partners II, L.P. and the manager of VHCP Co-Investment Holdings II, LLC. VHCP Management III, LLC is the general partner of Venrock Healthcare Capital Partners III, L.P. and the manager of VHCP Co-Investment Holdings III, LLC. VHCP Management EG, LLC is the general partner of Venrock Healthcare Capital Partners EG, L.P. Messrs. Shah and Koh are the voting members of VHCP Management II, LLC, VHCP Management III, LLC and VHCP Management EG, LLC.

Item 5. Ownership of Five Percent or Less of a Class

If this statement is being filed to report the fact that as of the date hereof the reporting person has ceased to be the beneficial owner of more than five percent of the class of securities, check the following ¨.

Item 6. Ownership of More than Five Percent on Behalf of Another Person

Not Applicable

Item 7. Identification and Classification of the Subsidiary Which Acquired the Security Being Reported on By the Parent Holding Company or Control Person.

Not Applicable

Item 8. Identification and Classification of Members of the Group

Not Applicable

Item 9. Notice of Dissolution of a Group

Not Applicable

Item 10. Certification

By signing below I certify that, to the best of my knowledge and belief, the securities referred to above were not acquired and are not held for the purpose of or with the effect of changing or influencing the control of the issuer of the securities and were not acquired and are not held in connection with or as a participant in any transaction having that purpose or effect, other than activities solely in connection with a nomination under § 240.14a-11. 

CUSIP No. 89532M101 Page 16 of 17

SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief, I certify that the information set forth in this statement is true, complete and correct.

Dated: April 21, 2022

Venrock Healthcare Capital Partners II, L.P.			Venrock Healthcare Capital Partners III, L.P.
By:	VHCP Management II, LLC		By:	VHCP Management III, LLC
Its:	General Partner		Its:	General Partner
By:	/s/ David L. Stepp		By:	/s/ David L. Stepp
	Name:	David L. Stepp		Name:	David L. Stepp
	Its:	Authorized Signatory		Its:	Authorized Signatory
VHCP Co-Investment Holdings II, LLC			VHCP Co-Investment Holdings III, LLC
By:	VHCP Management II, LLC		By:	VHCP Management III, LLC
Its:	Manager		Its:	Manager
By:	/s/ David L. Stepp		By:	/s/ David L. Stepp
	Name:	David L. Stepp		Name:	David L. Stepp
	Its:	Authorized Signatory		Its:	Authorized Signatory
VHCP Management II, LLC			VHCP Management III, LLC
By:	/s/ David L. Stepp		By:	/s/ David L. Stepp
	Name:	David L. Stepp		Name:	David L. Stepp
	Its:	Authorized Signatory		Its:	Authorized Signatory
Venrock Healthcare Capital Partners EG, L.P.			VHCP Management EG, LLC
By:	VHCP Management EG, LLC		/s/ David L. Stepp
Its:	General Partner		Name:	David L. Stepp
			Its:	Authorized Signatory
/s/ David L. Stepp
Name:	David L. Stepp
Its:	Authorized Signatory

Bong Koh

/s/ David L. Stepp

David L. Stepp, Attorney-in-fact

Nimish Shah

/s/ David L. Stepp

David L. Stepp, Attorney-in-fact

CUSIP No. 89532M101 Page 17 of 17

EXHIBITS

A: Joint Filing Agreement

B: Power of Attorney for Nimish Shah

C: Power of Attorney for Bong Koh

EXHIBIT A

JOINT FILING AGREEMENT

In accordance with Rule 13d-1(k) under the Securities Exchange Act of 1934, as amended, the undersigned agree to the joint filing on behalf of each of them of a statement on Schedule 13G (including amendments thereto) with respect to the Common Stock of Trevi Therapeutics, Inc. and further agree that this agreement be included as an exhibit to such filing. Each party to the agreement expressly authorizes each other party to file on its behalf any and all amendments to such statement. Each party to this agreement agrees that this joint filing agreement may be signed in counterparts.

In evidence whereof, the undersigned have caused this Agreement to be executed on their behalf this 21^st day of April, 2022.

Venrock Healthcare Capital Partners II, L.P.			Venrock Healthcare Capital Partners III, L.P.
By:	VHCP Management II, LLC		By:	VHCP Management III, LLC
Its:	General Partner		Its:	General Partner
By:	/s/ David L. Stepp		By:	/s/ David L. Stepp
	Name:	David L. Stepp		Name:	David L. Stepp
	Its:	Authorized Signatory		Its:	Authorized Signatory
VHCP Co-Investment Holdings II, LLC			VHCP Co-Investment Holdings III, LLC
By:	VHCP Management II, LLC		By:	VHCP Management III, LLC
Its:	Manager		Its:	Manager
By:	/s/ David L. Stepp		By:	/s/ David L. Stepp
	Name:	David L. Stepp		Name:	David L. Stepp
	Its:	Authorized Signatory		Its:	Authorized Signatory
VHCP Management II, LLC			VHCP Management III, LLC
By:	/s/ David L. Stepp		By:	/s/ David L. Stepp
	Name:	David L. Stepp		Name:	David L. Stepp
	Its:	Authorized Signatory		Its:	Authorized Signatory
Venrock Healthcare Capital Partners EG, L.P.			VHCP Management EG, LLC
By:	VHCP Management EG, LLC		/s/ David L. Stepp
Its:	General Partner		Name:	David L. Stepp
			Its:	Authorized Signatory

/s/ David L. Stepp
Name:	David L. Stepp
Its:	Authorized Signatory

Bong Koh

/s/ David L. Stepp

David L. Stepp, Attorney-in-fact

Nimish Shah

/s/ David L. Stepp

David L. Stepp, Attorney-in-fact

EXHIBIT B

POWER OF ATTORNEY FOR NIMISH SHAH

KNOW ALL BY THESE PRESENTS, that the undersigned hereby constitutes and appoints each of David L. Stepp, Sherman G. Souther and Lisa D. Harris signing individually, the undersigned’s true and lawful attorney-in fact and agent to:

(i) prepare execute and file, for and on behalf of the undersigned, any and all documents and filings that are required or advisable to be made with the United States Securities and Exchange Commission, any stock exchange or similar authority, under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations promulgated thereunder, including without limitation (a) any Joint Filing Agreement under Rule 13d-1(k) of the Exchange Act (or any successor provision thereunder), Schedule 13D and Schedule 13G (or any successor schedules or forms adopted under the Exchange Act ) and any amendments thereto in accordance with Section 13 of the Exchange Act and the rules thereunder, and (b) Forms 3, 4 and 5 and any amendments thereto in accordance with Section 16(a) of the Exchange Act and the rules thereunder; and

(ii) take any other action of any nature whatsoever in connection with the foregoing which, in the opinion of such attorney-in-fact, may be of benefit, in the best interest of, or legally required by, the undersigned, it being understood that the documents executed by such attorney-in-fact on behalf of the undersigned pursuant to this Power of Attorney shall be in such form and shall contain such terms and conditions as such attorney-in-fact may approve in such attorney-in-fact’s discretion.

The undersigned hereby grants to such attorney-in-fact full power and authority to do and perform any and every act and thing whatsoever requisite, necessary, or proper to be done in the exercise of any of the rights and powers herein granted, as fully to all intents and purposes as the undersigned might or could do if personally present, with full power of substitution or revocation, hereby ratifying and confirming all that such attorney-in-fact, or such attorney-in-fact’s substitute or substitutes, shall lawfully do or cause to be done by virtue of this power of attorney and the rights and powers herein granted. The undersigned acknowledges that the foregoing attorney-in-fact, in serving in such capacity at the request of undersigned, is not assuming, nor is Venrock assuming, any of the undersigned’s responsibilities to comply with the Exchange Act, including without limitation Sections 13 and 16 of the Exchange Act.

This power of Attorney shall remain in full force and effect until the earliest to occur of (a) the undersigned is no longer required to file any form or document with respect to the undersigned’s holdings of and transactions in securities issued by a company, (b) revocation by the undersigned in a signed writing delivered to the foregoing attorney-in-fact, or (c) until such attorney-in-fact shall no longer be employed by VR Management, LLC (or its successor).

IN WITNESS WHEREOF, the undersigned has cause this Power of Attorney to be executed as of this 21^st day of April, 2022.

/s/ Nimish Shah

EXHIBIT C

POWER OF ATTORNEY FOR BONG KOH

KNOW ALL BY THESE PRESENTS, that the undersigned hereby constitutes and appoints each of David L. Stepp, Sherman G. Souther and Lisa D. Harris signing individually, the undersigned’s true and lawful attorney-in fact and agent to:

(i) prepare execute and file, for and on behalf of the undersigned, any and all documents and filings that are required or advisable to be made with the United States Securities and Exchange Commission, any stock exchange or similar authority, under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations promulgated thereunder, including without limitation (a) any Joint Filing Agreement under Rule 13d-1(k) of the Exchange Act (or any successor provision thereunder), Schedule 13D and Schedule 13G (or any successor schedules or forms adopted under the Exchange Act ) and any amendments thereto in accordance with Section 13 of the Exchange Act and the rules thereunder, and (b) Forms 3, 4 and 5 and any amendments thereto in accordance with Section 16(a) of the Exchange Act and the rules thereunder; and

(ii) take any other action of any nature whatsoever in connection with the foregoing which, in the opinion of such attorney-in-fact, may be of benefit, in the best interest of, or legally required by, the undersigned, it being understood that the documents executed by such attorney-in-fact on behalf of the undersigned pursuant to this Power of Attorney shall be in such form and shall contain such terms and conditions as such attorney-in-fact may approve in such attorney-in-fact’s discretion.

The undersigned hereby grants to such attorney-in-fact full power and authority to do and perform any and every act and thing whatsoever requisite, necessary, or proper to be done in the exercise of any of the rights and powers herein granted, as fully to all intents and purposes as the undersigned might or could do if personally present, with full power of substitution or revocation, hereby ratifying and confirming all that such attorney-in-fact, or such attorney-in-fact’s substitute or substitutes, shall lawfully do or cause to be done by virtue of this power of attorney and the rights and powers herein granted. The undersigned acknowledges that the foregoing attorney-in-fact, in serving in such capacity at the request of undersigned, is not assuming, nor is Venrock assuming, any of the undersigned’s responsibilities to comply with the Exchange Act, including without limitation Sections 13 and 16 of the Exchange Act.

This power of Attorney shall remain in full force and effect until the earliest to occur of (a) the undersigned is no longer required to file any form or document with respect to the undersigned’s holdings of and transactions in securities issued by a company, (b) revocation by the undersigned in a signed writing delivered to the foregoing attorney-in-fact, or (c) until such attorney-in-fact shall no longer be employed by VR Management, LLC (or its successor).

IN WITNESS WHEREOF, the undersigned has cause this Power of Attorney to be executed as of this 21^st day of April, 2022.

/s/ Bong Koh