Exhibit 24
                               POWER OF ATTORNEY

        Know all by these presents, that the undersigned hereby constitutes and
appoints James C. Webster with full power of substitution, 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 U.S. Securities and Exchange Commission
            (the "SEC") a Form ID, including amendments thereto, and any other
            documents necessary or appropriate to obtain 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 (the "Exchange Act"), or any rule or regulation of
            the SEC;

        (2) execute for and on behalf of the undersigned, in the undersigned's
            capacity as an officer and/or director of Dril-Quip, Inc., a
            Delaware corporation (the "Company"), Forms 3, 4 and 5 in accordance
            with Section 16(a) of the Exchange Act and the rules thereunder, and
            any other forms or reports the undersigned may be required to file
            in connection with the undersigned's ownership, acquisition or
            disposition of securities of the Company;

        (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-
            fact's discretion.

        The undersigned hereby grants to 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 Exchange Act.

        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 attorney-in-fact.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 24th day of September, 2019.


                                                  /s/ Amy B. Schwetz
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                                                             Signature

                                                  Amy B. Schwetz
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