POWER OF ATTORNEY

      Know all by these present, that the undersigned hereby constitutes and
appoints each of Ankit Mahadevia. M.D., Satyavrat Shukla, Tamara Joseph, and
Meghan Small of Spero Therapeutics, Inc. (the "Company"). and Mathew J. Gardella
and Matthew W. Tikonoff of Mintz, Levin, Cohn, Ferris, Glovsky and Popeo, P.C.,
signing singly, with full power of substitution, the undersigned's true and
lawful attorney-in-fact to:

     (1)  execute for and on behalf of the undersigned, forms and authentication
          documents for EDGAR Filing Access;

     (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
          forms and authentication documents;

     (3)  execute for and on behalf of the undersigned, in the undersigned's
          capacity as an officer, director and/or 10% shareholder of the
          Company, Forms 3, 4, and 5 in accordance with Section 16(a) of the
          Securities and Exchange Act of 1934 and the rules thereunder;

     (4)  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 and timely file such form with the United States
          Securities and Exchange Commission and any stock exchange or similar
          authority; and

     (5)  take any other action of any type whatsoever in connection with the
          foregoing which, in the option of such attorney-in- fact, may be of
          benefit to, in the best interests 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 foregoing 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, 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 holding 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 on this 13th day of October, 2021.


                                    /s/ Kathleen Weldon Tregoning
                                    -------------------------------------
                                    Kathleen Weldon Tregoning