POWER OF ATTORNEY

       With respect to holdings of and transactions in securities issued by CSI
Compressco LP. (the "Company"), the undersigned hereby constitutes and appoints
the individuals named on Schedule A attached hereto and as may be amended from
time to time, or any of them signing singly, with full power of substitution and
resubstitution, to act as the undersigned's true and lawful attorney-in-fact to:

      1.   prepare, execute in the undersigned's name and on the undersigned's
  behalf, and submit to the United States Securities and Exchange Commission
  (the "SEC") a Form ID, including amendments thereto, and any other
  documents necessary or appropriate to obtain and/or regenerate codes and
  passwords enabling the undersigned to make electronic filings with the SEC of
  reports required by Section 16(a) of the Securities Exchange Act of 1934, as
  amended, or any rule or regulation of the SEC;

      2.   execute for and on behalf of the undersigned, Forms 3, 4, and 5 in
  accordance with Section 16 of the Securities Exchange Act of 1934, as amended,
  and the rules thereunder;

      3.   do and perform any and all acts for and on behalf of the undersigned
  which may be necessary or desirable to complete and execute any such Form 3,
  4, or 5, complete and execute any amendment or amendments thereto, and timely
  file such form with the SEC and any stock exchange or similar authority; and

      4.   take any other action of any type whatsoever in connection with the
  foregoing which, in the opinion of such attorney- in-fact, may be of benefit
  to, 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- facts discretion.

       The undersigned hereby grants to each 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 and resubstitution or revocation, hereby ratifying and confirming
all that such attorney-in- fact, or such attorneys-in- fact 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 attorneys-in- fact,
in serving in such capacity at the request of the undersigned, are not assuming,
nor is any Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934, as amended.

       This Power of Attorney shall remain in full force and effect until
the undersigned is no longer required to file Forms 3, 4, and 5 with respect to
the undersigned's holdings of and transactions in securities issued by the
Company, unless earlier revoked by the undersigned in a signed writing delivered
to the foregoing attorneys-in-fact.

       IN WITNESS WHEREOF, the undersigned has caused this Power of
Attorney to be executed as of this 31st day of October, 2022.

                                 By:   /s/ Michael James Tucker
                                 -------------------------------
                                 Name: Michael James Tucker



                                   Schedule A

      Individuals Appointed as Attorney-in-Fact with Full Power of Substitution
and Resubstitution

1.     Jonathan W. Byers

2.     Derek J. Anchondo


                                   Schedule A