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 August 10, 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:  August 10, 2004




                          M E D I A    R E L E A S E


FOR IMMEDIATE RELEASE

                    PRECISION DRILLING CORPORATION ANNOUNCES
                        CLOSING OF OVER-ALLOTMENT OPTION
--------------------------------------------------------------------------------

Calgary, Alberta, Canada August 10, 2004 - Precision Drilling Corporation
("Precision") is pleased to announce the closing of the over-allotment option
granted to the underwriters as part of its recent offering of common shares. The
over-allotment consists of an additional 400,000 common shares at a price of
US$49.80 per share, (CDN$65.25 per share), for gross proceeds of approximately
US$20 million. The over-allotment was exercised by a syndicate of underwriters
led by TD Securities Inc. and RBC Capital Markets. Precision expects to use the
net proceeds from the over-allotment for general corporate purposes.

A shelf registration statement relating to the common shares of Precision has
been filed with the Securities and Exchange Commission and has been declared
effective. This news release shall not constitute an offer to sell or the
solicitation of an offer to buy nor shall there be any sale of these securities
in the United States prior to registration and any sale in the United States
will be made by means of a prospectus that may be obtained from TD Securities
Inc. at 222 Bay Street, Ernst & Young Tower, 7th Floor, Toronto, Ontario, M1K
1A2 or from RBC Capital Markets at 200 Bay Street, Royal Bank Plaza, 4th Floor,
Toronto, Ontario, M5J 2W7.

Precision Drilling Corporation (TSX: PD and PD.U; 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