CCLP CSI Compressco LP

                                                           CSI Compressco GP LLC
Power of Attorney

Know all by these presents, that the undersigned hereby constitutes and appoints
Jonathan W. Byers and/or Derek J. Anchondo with full power of substitution and
resubstitution, as the undersigned's true and lawful attorney-in-fact to:

1.     execute for and on behalf of the undersigned, in the undersigned's
       capacity as an officer and/or director of CSI Compressco GP LLC (the
       "Company") Form ID and Forms 3, 4, and 5 (including amendments thereto)
       in accordance with Section 16(a) of the Securities Exchange Act of 1934,
       as amended, and the rules thereunder;

2.     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
       ID, 3, 4, or 5, complete and execute any amendment or amendments thereto,
       and timely file such form with the United States Securities and Exchange
       Commission and any stock exchange, self- regulatory association or any
       other authority, and provide a copy as required by law or as advisable to
       such persons as the attorney-in-fact deems appropriate; and

3.     take any other action of any type whatsoever in connection with the
       foregoing which, in the opinion of each 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-
       fact's 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 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 forgoing attorneys-in-fact, in
serving in such capacity at the request of the undersigned, are not assuming,
nor is the Company assuming, any of the undersigned's responsibilities to comply
with Section 16 of the Securities Exchange Act of 1934.

The undersigned further agrees that each such attorney-in-fact may rely entirely
on information furnished orally or in writing by or at the direction of the
undersigned to the attorney-in-fact. The undersigned also agrees to indemnify
and hold harmless the Company and each such attorney-in-fact against any
losses, claims, damages or liabilities (or actions in these respects) that arise
out of or are based upon any untrue statements or omissions of necessary facts
in the information provided by or at the direction of the undersigned, or upon
the lack of timeliness in the delivery of information by or at the direction of
the undersigned, to such attorney-in-fact for purposes of executing,
acknowledging, delivering or filing Form 3, 4 or 5 (including amendments
thereto).

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 (including
amendments thereto) with respect to the undersigned's holdings of and
transactions in securities issued by CSI Compressco LP, unless earlier revoked
by the undersigned in a signed writing delivered to the foregoing attorneys-in-
fact. This Power of Attorney revokes all other powers of attorney that the
undersigned has previously granted concerning the matters described herein.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 24 day of July, 2023.

/s/ Joseph P. McElroy
Signature
Print Name: Joseph Patrick McElroy

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