<PAGE>
 
                                                                     EXHIBIT 4.2

                                  DOLLAR NOTE

$20,000,000                     Houston, Texas                 February 10, 1997


     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 TWENTY MILLION DOLLARS ($20,000,000) (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 form 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 attorney's 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

<PAGE>
 
     This note is given in renewal, extension and rearrangement, and not in 
extinguishment, of that certain promissory note (the "Renewed Note") dated 
September 16, 1996, made by Drilex Systems, Inc., Drilex International Inc., 
Sharewell, Inc. and Cobb Directional Drilling Company, L.L.C., payable to the 
order of Payee and in the maximum principal amount of Fifteen Million Dollars 
($15,000,000).

     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

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


                                            DRILEX SYSTEMS, INC.,
                                            a Texas corporation


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

                                            SHAREWELL, INC.,
                                            a Delaware corporation


                                                 /s/ JOHN FORREST
                                            By: _______________________________
                                                John Forrest,
                                                Chief Executive Officer



                               Page 3 of 4 Pages
<PAGE>
 
                                  COBB DIRECTIONAL DRILLING COMPANY,
                                  L.L.C., a Delaware limited liability company

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


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

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


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



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