<PAGE>
 

                                  DOLLAR NOTE

$15,000,000                      Houston, Texas               September 16, 1996


     FOR VALUE RECEIVED, DRILEX INTERNATIONAL INC. (formerly Drilex Holdings
Corp.), a Delaware corporation, DRILEX SYSTEMS, INC., a Texas corporation,
SHAREWELL, INC. (formerly Shareco, Inc. ("Shareco")), a Delaware corporation,
and COBB DIRECTIONAL DRILLING COMPANY, L.L.C., a Delaware limited liability
company (collectively "Makers"), jointly and severally, promise to pay to the
order of TEXAS COMMERCE BANK NATIONAL ASSOCIATION ("Payee"), a national banking
association, at its principal banking building in the City of Houston, Harris
County, Texas, or at such other place as the holder of this note may hereafter
designate in writing, in immediately available funds and in lawful money of the
USA, the principal sum of FIFTEEN MILLION DOLLARS ($15,000,000) (or the unpaid
balance of all principal advanced against this note, if that amount is less),
together with interest on the unpaid principal balance of this note from time to
time outstanding until maturity at the rate or rates provided in the Interest
Rate Agreement of even date herewith among Payee and Makers (as amended,
supplemented and restated, the "Interest Rate Agreement") and interest on all
past due amounts, both principal and accrued interest, at the Past Due Rate;
provided that for the full term of this note the interest rate produced by the
aggregate of all sums paid or agreed to be paid to the holder of this note for
the use, forbearance or detention of the debt evidenced hereby shall not exceed
the Highest Lawful Rate.

     This note is the Dollar Note which has been issued pursuant to the terms of
that certain Amended and Restated Credit Agreement (as amended, supplemented and
restated, the "Credit Agreement") dated as of September 16, 1996 among Makers;
Drilex Systems Limited, and Payee, to which reference is made for all purposes.
Any term defined in the Credit Agreement and used in this note shall have the
meaning ascribed to it in the Credit Agreement.  Advances against this note by
Payee or other holder hereof shall be governed by the Credit Agreement and the
Interest Rate Agreement.  Payee is entitled to the benefits of and security
provided for in the Credit Agreement.  Such security includes those certain
Security Agreements of even date therewith between the respective Makers and
Payee.

     The principal of this note shall be due and payable on the Termination
Date, the final maturity of this note.  Accrued and unpaid interest shall be due
and payable as provided in the Interest Rate Agreement.

     Subject to the provisions of the Credit Agreement, Makers may at any time
pay the full amount or any part of this note without payment of any premium or
fee.

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     The unpaid principal balance of this note at any time shall be the total of
all principal lent or advanced against this note less the sum of all principal
payments and permitted prepayments made on this note by or for the account of
Makers.  All loans and advances and all payments and permitted prepayments made
hereon may be endorsed by the holder of this note on the schedule which is
attached hereto (and hereby made a part hereof for all purposes) or otherwise
recorded in the holder's records; provided that any failure to make notation of
(a) any advance shall not cancel, limit or otherwise affect Makers' obligations
or any holder's rights with respect to that advance, or (b) any payment or
permitted prepayment of principal shall not cancel, limit or otherwise affect
Makers' entitlement to credit for that payment as of the date received by the
holder.

     Subject to the provisions of the Credit Agreement, Makers may use all or
any part of the credit provided to be evidenced by this note at any time before
the Termination Date.  Makers may borrow, repay and reborrow and there is no
limit on the number of advances against this note so long as the total unpaid
principal at any time outstanding does not exceed the Dollar Available
Commitment.

     The occurrence of an Event of Default shall constitute default under this
note, whereupon the holder hereof may elect to exercise any or all rights,
powers and remedies afforded (a) under the Credit Documents and (b) by law,
including the right to accelerate the maturity of this entire note.

     If any holder of this note retains an attorney in connection with any such
default or to collect, enforce or defend this note or any papers intended to
secure or guarantee it in any lawsuit or in any probate, reorganization,
bankruptcy or other proceeding, or if Makers sue any holder in connection with
this note or any such papers and do not prevail, then Makers agree to pay to
each such holder, in addition to principal and interest, all reasonable costs
and expenses incurred by such holder in trying to collect this note or in any
such suit or proceeding, including reasonable attorneys' fees.

     Makers and any and all co-makers, endorsers, guarantors and sureties
severally waive notice (including, but not limited to, notice of intent to
accelerate and notice of acceleration, notice of protest and notice of
dishonor), demand, presentment for payment, protest, diligence in collecting and
the filing of suit for the purpose of fixing liability and consent that the time
of payment hereof may be extended and re-extended from time to time without
notice to any of them. Each such Person agrees that its liability on or with
respect to this note shall not be affected by any release of or change in any
guaranty or security at any time existing or by any failure to perfect or
maintain perfection of any lien against or security interest in any such
security or the partial or complete unenforceability of any guaranty or other
surety obligation, in each case in whole or in part, with or without notice and
before or after maturity.

                               Page 2 of 4 Pages
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     This note is given in renewal, extension and rearrangement, and not in
extinguishment, of that certain promissory note (the "Renewed Note") dated
September 29, 1995, made by Drilex Systems, Inc., Drilex Holdings Corp.,
Sharewell, Inc. and Cobb Directional Drilling Company, L.L.C., payable to the
order of Payee and in the maximum principal amount of Thirteen Million Dollars
($13,000,000).

     This note shall be governed by and construed in accordance with the laws of
the State of Texas and the USA from time to time in effect.  Harris County,
Texas shall be a proper place of venue for suit hereon.

                                       DRILEX INTERNATIONAL INC.,
                                       a Delaware corporation

                                       By: /s/ JOHN FORREST
                                          ------------------------------------- 
                                           John Forrest,
                                           President



                                       DRILEX SYSTEMS, INC.,
                                       a Texas corporation

                                       By: /s/ JOHN FORREST
                                          --------------------------------------
                                           John Forrest,
                                           President



                                       SHAREWELL, INC.,
                                       a Delaware corporation

                                       By: /s/ JOHN FORREST
                                          --------------------------------------
                                           John Forrest,
                                           Chief Executive Officer
                                 
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<PAGE>
 
                                    COBB DIRECTIONAL DRILLING COMPANY,
                                    L.L.C., a Delaware limited liability company

                                    By: Drilex International Inc.,
                                        a Delaware corporation,
                                        Member


                                        By: /s/ JOHN FORREST
                                           -------------------------------------
                                            John Forrest,
                                            President

                                    By: Drilex Systems, Inc.,
                                        a Texas corporation,
                                        Member


                                        By: /s/ JOHN FORREST
                                           -------------------------------------
                                            John Forrest,
                                            President

                               Page 4 of 4 Pages