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                                                                     EXHIBIT 4.4


                               AMENDING AGREEMENT


         WHEREAS Weatherford International, Inc., Weatherford Canada Ltd.,
Weatherford ER Acquireco Inc., Jamie E. Biluk, N. Scott A. Biluk, A. Lynn Biluk
and Tracey L. Biluk executed an exchange rights agreement (the "Exchange Rights
Agreement") dated as of December 19, 2001;

         AND WHEREAS, unless otherwise provided herein, the defined terms used
in this amending agreement shall have the same meanings attributed to such
defined terms in the Exchange Rights Agreement;

         AND WHEREAS WII has completed a merger transaction (the "Merger")
whereby, among other things, (i) Weatherford Merger, Inc. merged with and into
WII, (ii) WII became the surviving entity, (iii) WII became an indirect
subsidiary of Weatherford International Ltd. ("Weatherford Bermuda"), (iv) the
shares of WII Common Stock were converted, on a share for share basis, into the
right to receive common shares in the capital of Weatherford Bermuda (the
"Weatherford Bermuda Common Shares"), and (v) the Weatherford Bermuda Common
Shares were listed on The New York Stock Exchange;

         AND WHEREAS the parties hereto wish to amend the Exchange Rights
Agreement and certain other documents related thereto in order to reflect
certain aspects of the Merger;

         NOW THEREFORE for good and valuable consideration, the receipt and
sufficiency of which are acknowledged, the parties hereto hereby agree as
follows:

1. To the extent that the consent or approval of the Holders is required under
the Exchange Rights Agreement, the Support Agreement or the Exchangeable Share
Provisions (collectively the "ER Exchange Documents") with respect to the
Merger, the Holders hereby consent to and approve the Merger.

2. For the purposes of the ER Exchange Documents, effective as of 5:00 p.m.
(Eastern time) on June 26, 2002 (the "Merger Time"), (a) WII shall be replaced
by Weatherford Bermuda, and (b) the WII Common Stock shall be replaced by the
Weatherford Bermuda Common Shares.

3. In order to give further effect to section 2 hereof, effective as of the
Merger Time, the ER Exchange Documents including, without limitation, the
replacement sentence set out in section 5 below, are hereby amended in order to
substitute the words "Weatherford Bermuda" for the word "WII".

4. In order to give further effect to section 2 hereof, effective as of the
Merger Time, the ER Exchange Documents including, without limitation, the
replacement sentence set out in section 5 below, are hereby amended in order to
substitute the words "Weatherford Bermuda Common Shares" for the words "WII
Common Stock".

5. Effective as of the Merger Time, the second sentence set out in section 4.4
of the Exchange Rights Agreement is hereby deleted and replaced with the
following sentence:


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                                       2

                  "Concurrently with such Holder ceasing to be a holder of
                  Exchangeable Shares, the Holder, WCL and WII shall take all
                  actions necessary to ensure that the WII Common Stock
                  deliverable pursuant to such automatic exchange is delivered
                  prior to the Liquidation Event Effective Time and that the
                  Holder is registered as a shareholder of WII prior to the
                  Liquidation Event Effective Time such that the Holder is
                  entitled to participate with the other holders of WII Common
                  Stock in any distribution of assets in connection with any
                  such Liquidation Event."

6. Other than as provided in this amending agreement, the ER Exchange Documents
shall remain unamended and in full force and effect and the parties hereto
ratify and confirm the same.

7. This amending agreement shall enure to the benefit of and be binding upon the
parties hereto and their respective successors, administrators and assigns.

8. This amending agreement shall be governed by the laws of the Province of
Alberta.

9. Any amendment or supplement to this amending agreement shall be in writing
and shall be signed by the parties hereto.

10. This amending agreement may be executed in several counterparts, each of
which when so executed shall be deemed to an original but such counterparts
together shall constitute one and the same amending agreement.

11. A fax copy or telecopy of this amending agreement shall have the same force
and effect as an originally executed copy of this amending agreement.

12. This amending agreement has been executed by the parties hereto effective as
of the 26th day of June, 2002.

                                            WEATHERFORD INTERNATIONAL, INC.

                                            Per:     /s/  Burt M. Martin
                                                     ---------------------------
                                                     Burt M. Martin

                                            WEATHERFORD INTERNATIONAL LTD.

                                            Per:     /s/  Burt M. Martin
                                                     ---------------------------
                                                     Burt M. Martin

                                            WEATHERFORD CANADA LTD.

                                            Per:     /s/  Burt M. Marin
                                                     ---------------------------
                                                     Burt M. Martin

                                            WEATHERFORD ER ACQUIRECO INC.

                                            Per:     /s/  Burt M. Martin
                                                     ---------------------------
                                                     Burt M. Martin


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/s/ Dion Degrand                                    /s/  Jamie E. Biluk
-------------------------------                     ----------------------------
Witness                                             JAMIE E. BILUK

/s/ Lisa Tiller                                     /s/  N. Scott A. Biluk
-------------------------------                     ----------------------------
Witness                                             N. SCOTT A. BILUK

/s/ Lisa Tiller                                     /s/  A. Lynn Biluk
-------------------------------                     ----------------------------
Witness                                             A. LYNN BILUK

/s/ Cheryl Fontana                                  /s/  Tracey L. Biluk
-------------------------------                     ----------------------------
Witness                                             TRACEY L. BILUK