July 16, 2021

Via EDGAR Transmission

United States Securities and Exchange Commission

Division of Corporation Finance

100 F Street, N.E.

Washington, D.C. 20549

Re: Compass Therapeutics, Inc.: Registration Statement on Form S-3 filed July 9, 2021 (File No. 333-257821)

Ladies and Gentlemen:

Pursuant to Rule 461 under the Securities Act of 1933, as amended (the “Act”), Compass Therapeutics, Inc. (the “Company”) hereby requests that the effective date of the above-referenced registration statement (the “Registration Statement”) be accelerated to July 20, 2021, at 4:01 pm Eastern Time, or as soon thereafter as practicable, unless we or our outside counsel, Goodwin Procter LLP, request by telephone that such Registration Statement be declared effective at some other time. In making this acceleration request, the Company acknowledges that it is aware of its responsibilities under the Act.

If you have any questions regarding this request, please contact James Xu of Goodwin Procter LLP at (415) 533-5887.

Sincerely,

Compass Therapeutics, Inc.

/s/ Vered Bisker-Leib

Vered Bisker-Leib

President and Chief Operating Officer

cc: Vered Bisker-Leib, Compass Therapeutics, Inc.

Neil Lerner, Compass Therapeutics, Inc.

Richard Hoffman, Esq., Goodwin Procter LLP

James Xu, Esq., Goodwin Procter LLP