Exhibit (a)(1)(iii)

Offer by
TORTOISE ENERGY INDEPENDENCE FUND, INC.
To Purchase for Cash
up to 5% of the Fund’s Outstanding
Shares of Common Stock

THE OFFER TO PURCHASE WILL EXPIRE ON NOVEMBER 1, 2023 AT 5:00 P.M.,
NEW YORK CITY TIME UNLES THE OFFER TO PURCHASE IS EXTENDED.

THIS OFFER IS NOT CONDITIONED ON ANY MINIMUM NUMBER OF SHARES
BEING TENDERED, BUT IS SUBJECT TO OTHER CONDITIONS AS OUTLINED IN
THE OFFER TO PURCHASE AND IN THE LETTER OF TRANSMITTAL.

October 2, 2023

To Brokers, Dealers, Commercial Banks,

Trust Companies and Other Nominees:

We are enclosing herewith the material listed below relating to the offer of Tortoise Energy Independence Fund, Inc., a Maryland corporation registered under the Investment Company Act of 1940, as amended, as a closed-end, non-diversified management investment company (the “Fund”), to purchase up to 5% of the Fund’s outstanding shares of Common Stock, par value $0.001 per share (the “Shares”), upon the terms and conditions set forth in the Offer to Purchase dated October 2, 2023 and in the related Letter of Transmittal (which together constitute the “Purchase Offer”). The price to be paid for the Shares is an amount per Share, equal to 98% of the net asset value per Share as determined by the Fund at the close of regular trading on the New York Stock Exchange on November 1, 2023 (the “Purchase Pricing Date”).

Tortoise Capital Advisors, L.L.C. (“Tortoise”) serves as the Fund’s Investment Manager. Tortoise is a limited liability company organized under the laws of Delaware on October 4, 2002 and a registered investment adviser under the Investment Advisers Act of 1940. The principal business address of Tortoise is 6363 College Boulevard, Suite 100A, Overland Park, KS 66211.

We are asking you to contact your clients for whom you hold Shares registered in your name (or in the name of your nominee) or who hold Shares registered in their own names. Please bring the Purchase Offer to their attention as promptly as possible. No fees or commission will be payable to brokers, dealers or other persons for soliciting tenders of Shares pursuant to the Offer. The Fund will, upon request, reimburse you for reasonable and customary mailing and handling expenses incurred by you in forwarding any of the enclosed materials to your clients. The Fund will pay all transfer taxes on its purchase of Shares, subject to Instruction 7, “Stock Transfer Taxes,” of the Letter of Transmittal. However, backup withholding at a 24% rate may be required unless either an exemption is proved or the required taxpayer identification information and certifications are provided. See Section 15, “Certain Federal Income Tax Consequences,” of the Offer to Purchase and Instruction 11, “Backup Withholding,” of the Letter of Transmittal.

The Fund’s Shares have at times traded at a premium to the Fund’s net asset value per Share. It may not be in a Stockholder’s interest to tender Shares in connection with the Purchase Offer if the Shares are trading at a premium. The market price of the Shares can and does fluctuate. Accordingly, on the Purchase Pricing Date, the market price of the Shares may be above or below the Fund’s net asset value per Share.

For your information and for forwarding to your clients, we are enclosing the following documents:

1. A letter to Stockholders of the Fund from P. Bradley Adams, Chief Executive Officer of the Fund;

2. The Offer to Purchase, dated October 2, 2023;

3. The Letter of Transmittal for your use and to be provided to your clients;

4. Notice of Guaranteed Delivery;

5. Form of letter to clients that may be sent to your clients for whose accounts you hold Shares registered in your name (or in the name of your nominee).

The Purchase Offer is not being made to, nor will the Fund accept tenders from, holders of Shares in any state or other jurisdiction in which the Purchase Offer would not be in compliance with the securities or Blue Sky laws of such jurisdiction.

As described in the Fund’s Offer to Purchase under Section 5, “Procedure for Tendering Shares,” tenders may be made without the concurrent deposit of stock certificates if (1) such tenders are made by or through a broker or dealer that is a member firm of a registered national securities exchange or a member of the Financial Industry Regulatory Authority, Inc. or a commercial bank or trust company having an office, branch, or agency in the United States; and (2) certificates for Shares (or a confirmation of a book-entry transfer of such Shares into the Depositary’s account at a Book-Entry Transfer Facility (as defined in the Letter of Transmittal)), together with a properly completed and duly executed Letter of Transmittal, and any other documents required by the Letter of Transmittal, are received by the Depositary within two business days after receipt by the Depositary of a properly completed and duly executed Notice of Guaranteed Delivery.

As described in the Offer to Purchase, if more than 5% of the Fund’s outstanding Shares are duly tendered prior to the Expiration Date, the Fund will purchase Shares tendered on a pro rata basis.

Neither the Fund, its Board of Directors nor the Investment Manager to the Fund makes any recommendation to any Stockholder whether to tender any Shares.

For additional information or copies of the enclosed material, please contact Georgeson LLC (the “Information Agent”) toll free at 1-866-432-2791.

Very truly yours,

P. Bradley Adams
Chief Executive Officer

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL CONSTITUTE YOU OR ANY OTHER PERSON THE AGENT OF THE TORTOISE ENERGY INDEPENDENCE FUND, INC., THE INFORMATION AGENT, OR THE DEPOSITARY OR AUTHORIZE YOU OR ANY OTHER PERSON TO MAKE ANY STATEMENTS OR USE ANY MATERIAL ON THEIR BEHALF WITH RESPECT TO THE OFFER, OTHER THAN THE MATERIAL ENCLOSED HEREWITH AND THE STATEMENTS SPECIFICALLY SET FORTH IN SUCH MATERIAL.