UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER
                   PURSUANT TO SECTION 13a-16 OR 15d-16 OF THE
                         SECURITIES EXCHANGE ACT OF 1934

                                 For May 21, 2004

                        Commission File Number: 001-14534


                         PRECISION DRILLING CORPORATION
             (Exact name of registrant as specified in its charter)


                           4200, 150 - 6TH AVENUE S.W.
                                CALGARY, ALBERTA
                                 CANADA T2P 3Y7
                    (Address of principal executive offices)


         Indicate by check mark whether the registrant files or will file annual
reports under cover Form 20-F or Form 40-F.

                    Form 20-F [_]               Form 40-F   [X]

         Indicate by check mark if the registrant is submitting the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(1). _______

         Note: Regulation S-T Rule 101(b)(1) only permits the submission in
paper of a Form 6-K if submitted solely to provide an attached annual report to
security holders.

         Indicate by check mark if the registrant is submitting the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(7):_______

         Note: Regulation S-T Rule 101(b)(7) only permits the submission in
paper of a Form 6-K if submitted to furnish a report or other document that the
registrant foreign private issuer must furnish and make public under the laws of
the jurisdiction in which the registrant is incorporated, domiciled or legally
organized (the registrant's "home country"), or under the rules of the home
country exchange on which the registrant's securities are traded, as long as the
report or other document is not a press release, is not required to be and has
not been distributed to the registrant's security holders, and, if discussing a
material event, has already been the subject of a Form 6-K submission or other
Commission filing on EDGAR.

         Indicate by check mark whether the registrant by furnishing the
information contained in this Form is also thereby furnishing the information to
the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of
1934.
                          Yes [_]                   No   [X]

         If "Yes" is marked, indicate below the file number assigned to the
registrant in connection with Rule 12g3-2(b): 82-  N/A
                                                 ---------




Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.



                                         PRECISION DRILLING CORPORATION



                                         Per: /s/ Jan M. Campbell
                                              ------------------------
                                              Jan M. Campbell
                                              Corporate Secretary



Date:  May 21, 2004





                                  NEWS RELEASE



   FOR IMMEDIATE RELEASE

                    PRECISION DRILLING CORPORATION SUBSIDIARY
               ACQUIRES 99.7% OF REEVES OILFIELD SERVICES LIMITED

   Calgary, Alberta, Canada, May 21, 2004 - Precision Drilling Corporation
   ("Precision") announces that its wholly owned subsidiary, Precision Holdings
   (UK) Limited, has acquired 99.7% of the issued and outstanding shares of UK
   based Reeves Oilfield Services Limited ("Reeves") pursuant to its previously
   announced offer to acquire all of the issued and outstanding shares of Reeves
   (the "Offer") for (pound)92.4 million, ((pound)88.4 million net of cash
   acquired, equivalent to Cdn. $218 million). The Offer will remain open for
   acceptance until June 10, 2004. A 100% shareholding is sought, whether this
   be achieved through 100% eventual acceptances or use of the mandatory buy-out
   mechanism provided in the Companies Act 1985 (United Kingdom).

   Reeves' premier offering consists of a highly reliable formation evaluation
   logging system that may be conveyed on wireline or using an array of
   conveyance alternatives such as drill pipe, tractors, or coil tubing. The
   Reeves system design enables high quality logging data to be recorded more
   efficiently than current competitors' offerings.

   Precision Drilling Corporation (TSX: PD, and PDU; NYSE: PDS) is a global
   oilfield services company providing a broad range of drilling, production and
   evaluation services with focus on fulfilling customer needs through
   fit-for-purpose technologies for the maturing oilfields of the 21st century.
   With corporate offices in Calgary, Alberta, Canada and Houston, Texas, and
   research facilities in the U.S. and Europe, Precision employs more than
   10,000 people conducting operations in more than 30 countries. Precision is
   committed to providing efficient and safe services to create value for our
   customers, our shareholders and our employees.

   FOR FURTHER INFORMATION PLEASE CONTACT HANK B. SWARTOUT, CHAIRMAN, PRESIDENT
   AND CHIEF EXECUTIVE OFFICER, OR DALE E. TREMBLAY, SENIOR VICE PRESIDENT
   FINANCE AND CHIEF FINANCIAL OFFICER, 4200, 150 - 6TH AVENUE S.W., CALGARY,
   ALBERTA T2P 3Y7, TELEPHONE (403) 716-4500; FAX (403) 264-0251; WEBSITE:
   WWW.PRECISIONDRILLING.COM