<PAGE>   1


                                                                   EXHIBIT 10.16


THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE SOLD OR TRANSFERRED
EXCEPT PURSUANT TO AN EXEMPTION FROM, OR OTHERWISE IN A TRANSACTION NOT SUBJECT
TO, THE REGISTRATION REQUIREMENTS OF SUCH ACT. IN ADDITION, THE SECURITIES
REPRESENTED HEREBY ARE SUBJECT TO THE LIMITATIONS ON TRANSFER SET FORTH IN THE
STOCKHOLDERS AGREEMENT, DATED AUGUST 11, 1997, AMONG THE CORPORATION, THE
PURCHASER, AND THE STOCKHOLDERS IDENTIFIED THEREIN. A COPY OF THE STOCKHOLDERS
AGREEMENT IS AVAILABLE FOR INSPECTION AT THE PRINCIPAL OFFICE OF THE CORPORATION
AND WILL BE FURNISHED WITHOUT CHARGE TO THE HOLDER HEREOF UPON WRITTEN REQUEST
TO THE CORPORATION.


                            W-H ENERGY SERVICES, INC.



                                                             Warrant to Purchase
                                                                18,906.25 Shares
                                                                 of Common Stock

                                                                 October 1, 1998

                          Common Stock Purchase Warrant

         THIS Common Stock Purchase Warrant (the "Warrant") CERTIFIES that, for
value received, W-H INVESTMENT II, G.P., a general partnership ("Assignee"), is
entitled to purchase from W-H ENERGY SERVICES, INC., a Texas corporation
formerly known as W-H Holdings, Inc. (the "Corporation"), 18,906.25 shares of
the Class A Common Stock, $1.00 par value per share (the "Common Stock"), of the
Corporation, representing 4.822% of the Common Stock outstanding on a Fully
Diluted Basis at the price (the "Exercise Price") of $73.00 per share, subject
to adjustment, in each case, as provided herein, at any time or from time to
time during the period commencing on the date hereof and ending at 5:00 P.M. on
the tenth anniversary of the date hereof (the "Expiration Date").

         This Warrant has been issued pursuant to an Assignment, dated as of
October 1, 1998, (the "Assignment") between the Assignee and W-H INVESTMENT,
L.P., a Delaware limited partnership ("Assignor"), under which Assignor
assigned to Assignee certain rights under a warrant issued to Assignor pursuant
to (i) the Agreement and Plan of Recapitalization (the "Recapitalization
Agreement") dated August 11, 1997, between the Corporation, the Assignor and the
stockholders identified therein, (ii) the Subscription Agreement (the
"Subscription Agreement") dated August 11, 1997, between the Corporation and the
Assignor, and (iii) the Stockholders Agreement ("Stockholders Agreement") dated
August 11, 1997, between the Corporation, the Assignor and the stockholders
identified therein, and is subject to the terms and conditions, and entitled to
the benefits, thereof, including provisions providing certain information and
other rights. Copies of the Assignment, the Recapitalization Agreement, the


<PAGE>   2


Subscription Agreement and the Stockholders Agreement are available for
inspection at the principal office of the Corporation and will be furnished
without charge to the Holder upon written request to the Corporation.
Capitalized terms used but not defined herein shall have the meaning given to
them in the Recapitalization Agreement.

                                    ARTICLE I

                                   DEFINITIONS

         Section 1.1 Definitions. As used in this Agreement, the following terms
shall have the following meanings:

         "Assignment Form" shall mean the assignment form attached as Annex 2
hereto.

         "Common Stock" shall mean the Class A Common Stock, $1.00 par value, of
the Corporation having the terms, conditions, rights and limitations described
in Exhibit A hereto.

         "Closing Date" shall mean October 1, 1998.

         "Corporation" shall have the meaning given to such term in the
Preamble.

         "Delivery Date" shall have the meaning given to such term in Section
3.2.

         "Exchange Act" shall mean the Securities Exchange Act of 1934, as
amended.

         "Exchange Form" shall mean the exchange form attached as Annex 3
hereto.

         "Excluded Securities" shall mean:

         (i) shares of capital stock issued pursuant to a stock dividend or a
stock split or other subdivision of shares;

         (ii) Common Stock issued upon exercise of the Warrant;

         (iii) securities issued by the Corporation in a Qualified Public
Offering;

         (iv) securities issued pursuant to the direct or indirect bona fide
acquisition by the Corporation of any Person that is not an Affiliate, whether
by merger, purchase of stock, purchase of assets or otherwise; and

         (v) Common Stock issued under the New Management Option Plan.

         "Executive Officer" shall mean, with respect to the Corporation, its
President, Chief Financial Officer or Treasurer or Vice President.

         "Exercise Form" shall mean the exercise form attached as Annex 1
hereto.

         "Exercise Price" shall mean $73.00 per share of Common Stock, subject
to adjustment from time to time in the manner provided in Section 3.4.


                                      -2-
<PAGE>   3


         "Expiration Date" shall mean August 11, 2007.

         "Financial Officer" shall mean the Chief Financial Officer, Treasurer
or Assistant Treasurer of the Corporation.

         "Fully Diluted Basis" means, as applied to the calculation of the
number of shares of Common Stock outstanding at any time, after giving effect to
(a) all shares of Common Stock outstanding at the time of determination, (b) all
shares of Common Stock issuable upon the exercise of any option, warrant
(including the Warrants and the options issuable or issued under the New
Management Option Plan) or similar right to purchase Common Stock outstanding at
the time of determination and then exercisable at a per share price equal to or
less than the price per share of Common Stock being determined and (c) all
shares of Common Stock issuable upon the conversion or exchange of any security
convertible into or exchangeable for shares of Common Stock outstanding at the
time of determination and then so convertible or exchangeable at a conversion or
exchange price equal to or less than the price per share of Common Stock being
determined. Such calculation will not be made in accordance with the "treasury
method."

         "Holder" shall have the meaning given to such term in Section 2.1.

         "NASDAQ" shall mean the NASDAQ National Market or the NASDAQ Smallcap
Market.

         "Publicly Traded" shall mean, with respect to any security, that such
security is (a) listed on a domestic securities exchange, (b) quoted on NASDAQ
or (c) traded in the domestic over-the-counter market, which trades are reported
by the National Quotation Bureau, Incorporated.

         "Qualified Public Offering" shall have the meaning ascribed thereto in
the Corporations' Stockholders Agreement as in effect at the date hereof.

         "Requisite Holders" shall mean Holders holding Warrants or Warrant
Shares representing at least 51 % of all Warrant Shares issued or issuable upon
exercise of the Warrant outstanding on the date of determination.

         "Warrant" shall have the meaning given to such term in the preamble.

         "Warrant Register" shall have the meaning given to such term in Section
2.1.

         "Warrant Shares" shall mean (a) the shares of Common Stock issued or
issuable upon exercise of a Warrant in accordance with Section 3.1 or upon
exchange of a Warrant in accordance with Section 2.2 and (b) any securities of
the Corporation distributed with respect to the securities referred to in the
preceding clause (a). As used in this Agreement, the phrase "Warrant Shares then
held" by any Holder or Holders shall mean Warrant Shares held at the time of
determination by such Holder or Holders, and shall include Warrant Shares
issuable upon exercise of Warrants held at the time of determination by such
Holder or Holders.

         Section 1.2 Interpretation. Unless the context of this Agreement
clearly requires otherwise, references to the plural include the singular, to
the singular include the plural,


                                      -3-
<PAGE>   4


and to the part include the whole. The term "including" is not limiting and the
term "or" has the inclusive meaning represented by the term "and/or." The words
"hereof," "herein," "hereunder," and similar terms in this Agreement refer to
this Agreement as a whole and not to any particular provision of this Agreement.
References to "Articles", "Sections," "Subsections," "Exhibits," and "Schedules"
are to Articles, Sections, Subsections, Exhibits and Schedules, respectively, of
this Agreement, unless otherwise specifically provided. Terms defined herein may
be used in the singular or the plural. Any capitalized terms used herein which
are not specifically defined herein have the meaning given to them in the
Recapitalization Agreement.

                                   ARTICLE II

                  FORM; EXCHANGE FOR WARRANTS; TRANSFER; TAXES

         Section 2.1 Warrant Register. Each Warrant issued, exchanged or
transferred pursuant to the Recapitalization Agreement shall be registered in a
warrant register (the "Warrant Register"). The Warrant Register shall set forth
the number of each Warrant, the name and address of the holder (a "Holder")
thereof, and the original number of Warrant Shares purchasable upon the exercise
thereof. The Warrant Register will be maintained by the Corporation and will be
available for inspection by any Holder at the principal office of the
Corporation or such other location as the Corporation may designate to the
Holders in the manner set forth in this Agreement. The Corporation shall be
entitled to treat the Holder of any Warrant as the owner in fact thereof for all
purposes and shall not be bound to recognize any equitable or other claim to or
interest in such Warrant on the part of any other person. The Corporation shall
not be liable for complying with a request by a fiduciary or nominee of a
fiduciary to register a transfer of any Warrant which is registered in the name
of such fiduciary or nominee, unless made with the actual knowledge that such
fiduciary or nominee is committing a breach of trust in requesting such
registration of transfer, or with knowledge of such facts that the Corporation's
participation therein amounts to bad faith.

         Section 2.2 Exchange of Warrants for Warrants. (a) The Holder may
exchange this Warrant for another Warrant or Warrants of like kind and tenor
representing in the aggregate the right to purchase the same number of Warrant
Shares which could be purchased pursuant to the Warrant being so exchanged. In
order to effect an exchange permitted by this Section 2.2, the Holder shall
deliver to the Corporation such Warrant accompanied by an Exchange Form in the
form attached hereto as Annex 3 signed by the Holder thereof specifying the
number and denominations of Warrants to be issued in such exchange and the names
in which such Warrants are to be issued. Within ten (10) Business Days of
receipt of such a request, the Corporation shall issue, register and deliver to
the Holder thereof each Warrant to be issued in such exchange.

         (b) Upon receipt of evidence reasonably satisfactory to the Corporation
(an affidavit of the Holder being satisfactory) of the ownership and the loss,
theft, destruction or mutilation of any Warrant, and in the case of any such
loss, theft or destruction, upon receipt of an indemnity reasonably satisfactory
to the Corporation (if the Holder is a creditworthy financial institution or
other creditworthy institutional investor its own agreement being satisfactory)
or, in the case of any such mutilation, upon surrender of such Warrant, the
Corporation shall (at its expense) execute and deliver in lieu of such Warrant a
new Warrant of like kind representing the same rights represented by and dated
the date of such lost, stolen, destroyed or mutilated


                                      -4-
<PAGE>   5


Warrant. Any such new Warrant shall constitute an original contractual
obligation of the Corporation, whether or not the allegedly lost, stolen,
mutilated or destroyed Warrant shall be at any time enforceable by any Person.

         (c) The Corporation shall pay all taxes (other than any applicable
income or similar taxes payable by a Holder of a Warrant) attributable to an
exchange of a Warrant pursuant to this Section 2.2; provided, however, that the
Corporation shall not be required to pay any tax which may be payable in respect
of any transfer involved in the issuance of any Warrant in a name other than
that of the Holder of the Warrant being exchanged.

         Section 2.3 Transfer of Warrant. (a) Subject to Section 2.3(c) hereof
and the Subscription Agreement and Stockholders Agreement, each Warrant may be
transferred by the Holder thereof by delivering to the Corporation such Warrant
accompanied by a properly completed Assignment Form in the form of Annex 2.
Within ten (10) Business Days of receipt of such Assignment Form the Corporation
shall issue, register and deliver to the Holder, subject to Section 2.3(c)
hereof, a new Warrant or Warrants of like kind and tenor representing in the
aggregate the right to purchase the same number of Warrant Shares which could be
purchased pursuant to the Warrant being transferred. In all cases of transfer by
an attorney, the original power of attorney, duly approved, or a copy thereof,
duly certified, shall be deposited and remain with the Corporation. In case of
transfer by executors, administrators, guardians or other legal representatives,
duly authenticated evidence of their authority shall be produced and may be
required to be deposited and remain with the Corporation in its discretion.

         (b) Each Warrant issued in accordance with this Section 2.3 shall bear
the restrictive legend set forth on the face of this Warrant, unless the Holder
or transferee thereof supplies to the Corporation an opinion of counsel,
reasonably satisfactory to the Corporation, that the restrictions described in
such legend are no longer applicable to such Warrant.

         (c) The transfer of Warrants and Warrant Shares shall be permitted, so
long as such transfer is pursuant to a transaction that complies with, or is
exempt from, the provisions of the Securities Act, and the Corporation may
require an opinion of counsel (which may be internal counsel to a Holder) in
form and substance reasonably satisfactory to it to such effect prior to
effecting any transfer of Warrants or Warrant Shares.

                                  ARTICLE III

                EXERCISE OF WARRANT; EXCHANGE FOR WARRANT SHARES

         Section 3.1 Exercise of Warrants. On any Business Day prior to the
Expiration Date, a Holder may exercise a Warrant, in whole or in part, by
delivering to the Corporation such Warrant accompanied by a properly completed
Exercise Form in the form of Annex 1 and a check in an aggregate amount equal to
the product obtained by multiplying (a) the Exercise Price by (b) the number of
Warrant Shares being purchased; provided, however, in the event the Holder
exercises this Warrant in connection with or immediately prior to a sale by the
Holder of Warrant Shares, in lieu of paying the applicable Exercise Price
therefor, the Holder may elect to receive that number of Warrant Shares which is
equal to the number of shares for which this Warrant is being exercised less the
number of shares having a fair market value (determined by



                                      -5-
<PAGE>   6


reference to the price per share at which the Holder is selling the Warrant
Shares) equal to such applicable Exercise Price. Any partial exercise of a
Warrant shall be for a whole number of Warrant Shares only.

         Section 3.2 Issuance of Common Stock. (a) Within ten (10) Business Days
following the delivery date (the "Delivery Date") of (i) an Exercise Form or
Exchange Form in accordance with Section 3.1 or 3.2, (ii) a Warrant and (iii)
any required payments of the Exercise Price, the Corporation shall issue and
deliver to the Holder a certificate or certificates, registered in the name or
names set forth on such notice, representing the Warrant Shares being purchased
or to be received upon such exchange.

         (b) If a Holder shall exercise or exchange a Warrant for less than all
of the Warrant Shares which could be purchased or received thereunder, the
Corporation shall issue to the Holder, within ten (10) Business Days of the
Delivery Date, a new Warrant evidencing the right to purchase the remaining
Warrant Shares. Each Warrant surrendered pursuant to Section 3.1 shall be
canceled.

         (c) The Corporation shall pay all taxes (other than any applicable
income or similar taxes payable by a Holder of a Warrant) attributable to the
initial issuance of Warrant Shares upon the exercise or exchange of a Warrant;
provided, however, that the Corporation shall not be required to pay any tax
which may be payable in respect of any transfer involved in the issuance of any
Warrant or any certificate for Warrant Shares in a name other than that of the
Holder of the Warrant being exercised or exchanged.

         (d) The person in whose name any certificate for shares of Common Stock
is issued upon exercise or exchange of a Warrant shall for all purposes be
deemed to have become the holder of record of such shares on the Delivery Date,
irrespective of the date of delivery of such certificate, except that, if the
Delivery Date is a date when the stock transfer books of the Corporation are
closed, such person shall be deemed to have become the holder of record of such
shares at the close of business on the next succeeding date on which the stock
transfer books are open.

         (e) If any shares of Common Stock required to be reserved for purposes
of the exercise or exchange of a Warrant require registration or approval under
any applicable law, the Corporation will in good faith and as expeditiously as
possible cause such shares to be registered or seek such approval, as
applicable. The Corporation may suspend the exercise of any Warrant so affected
for the period during which such registration or approval is required but not in
effect.

         Section 3.3 Adjustment of Exercise Price and Number of Warrant Shares.
The number and kind of Warrant Shares purchasable upon exercise of each Warrant
shall be subject to adjustment from time to time in accordance with this Section
3.3.

         Section 3.3.1 Subdivisions or Combinations of Common Stock. If, at any
time after the Closing Date, (a) the number of shares of Common Stock
outstanding is increased by a dividend or other distribution payable in shares
of Common Stock or by a subdivision or split-up of shares of Common Stock or (b)
the number of shares of Common Stock outstanding is decreased by a combination
or reverse stock split of shares of Common Stock, then, in each case,


                                      -6-
<PAGE>   7


effective as of the effective date of such event retroactive to the record date,
if any, of such event, (i) the Exercise Price shall be adjusted to a price
determined by multiplying (A) the Exercise Price in effect immediately prior to
such event by (B) a fraction, the numerator of which shall be the number of
shares of Common Stock outstanding immediately prior to such event and the
denominator of which shall be the number of shares of Common Stock outstanding
after giving effect to such event, and (ii) the number of Warrant Shares subject
to purchase upon the exercise of any Warrant shall be adjusted effective at such
time, to a number equal to the product of (A) the number of Warrant Shares
subject to purchase upon the exercise of such Warrant immediately prior to such
event by (B) a fraction, the numerator of which shall be the number of shares of
Common Stock outstanding on a Fully Diluted Basis after giving effect to such
event and the denominator of which shall be the number of shares of Common Stock
outstanding on a Fully Diluted Basis immediately prior to such event.

         Section 3.3.2 Capital Reorganization or Capital Reclassifications. If,
at any time after the Closing Date, there shall be any capital reorganization or
any reclassification of the capital stock of the Corporation (other than a
change in par value or from par value to no par value or from no par value to
par value or as a result of a stock dividend or subdivision, split-up or
combination of shares), then in each case the Corporation shall cause effective
provision to be made so that each Warrant shall, effective as of the effective
date of such event retroactive to the record date, if any, of such event, be
exercisable or exchangeable for the kind and number of shares of stock, other
securities, cash or other property to which a holder of the number of shares of
Common Stock deliverable upon exercise or exchange of such Warrant would have
been entitled upon such reorganization or reclassification and any such
provision shall include adjustments in respect of such stock, securities or
other property that shall be as nearly equivalent as may be practicable to the
adjustments provided for in this Agreement with respect to such Warrant.

         Section 3.3.3 Consolidations and Mergers. If, at any time after the
Closing Date, the Corporation shall consolidate with, merge with or into, or
sell all or substantially all of its assets or property to, another corporation,
then the Corporation shall cause effective provision to be made so that each
Warrant shall, effective as of the effective date of such event retroactive to
the record date, if any, of such event, be exercisable or exchangeable for the
kind and number of shares of stock, other securities, cash or other property to
which a holder of the number of shares of Common Stock deliverable upon exercise
or exchange of such Warrant would have been entitled upon such event.

         Section 3.3.4 Notice; Calculations; Etc. Whenever the Exercise Price
and the number of Warrant Shares shall be adjusted as provided in this Section
3.3, the Corporation shall provide to each Holder a statement, signed by an
Executive Officer, describing in detail the facts requiring such adjustment and
setting forth a calculation of the Exercise Price and the number of Warrant
Shares applicable to each Warrant after giving effect to such adjustment. All
calculations under this Section 3.3 shall be made to the nearest one hundredth
of a cent ($.0001) or to the nearest one-tenth of a share, as the case may be.

         Section 3.3.5 Excluded Transactions. Notwithstanding any other
provision of this Warrant, no adjustment shall be made pursuant to this Section
3.3 in respect of the issuance of Excluded Securities.



                                      -7-
<PAGE>   8


                                   ARTICLE IV

                              CERTAIN OTHER RIGHTS

         Section 4.1 Payments in Respect of Dividends and Distributions. If, at
any time prior to the earlier of (i) the Expiration Date and (ii) the
consummation of a Qualified Public Offering, the Corporation pays any dividend
or makes any distribution (whether in cash, property or securities of the
Corporation) on its capital stock which does not result in an adjustment under
Section 3, then the Corporation shall simultaneously pay to the Holder of each
Warrant, the dividend or distribution which would have been paid to such Holder
on the Warrant Shares receivable upon the exercise in full of such Warrant had
such Warrant been fully exercised immediately prior to the record date for such
dividend or distribution or, if no record is taken, the date as of which the
record holders of Common Stock entitled to such dividend or distribution are to
be determined.

         Section 4.2 Fiduciary Duties of the Corporation. The Corporation and
its directors shall owe the holders of the Warrants the same fiduciary duties
that the Corporation and its directors would owe to the Warrant Shares
underlying the Warrants.

                                   ARTICLE V

                                 MISCELLANEOUS

         Section 5.1 Notices. All notices, demands and requests of any kind to
be delivered to any party hereto in connection with this Agreement shall be in
writing (i) delivered personally, (ii) sent by nationally-recognized overnight
courier, (iii) sent by first class, registered or certified mail, return receipt
requested or (iv) sent by facsimile, in each case to such party at its address
as follows:

         (a)   if to the Corporation, to:

               W-H Energy Services, Inc.
               10370 Richmond Avenue
               Suite 990
               Houston, TX 77042
               Telephone: (713) 974-9071
               Telecopier: (713) 974-7029

               with a copy to:

               The Jordan Company
               767 Fifth Avenue, 48th Floor
               New York, NY 10153
               Attention: Jonathan F. Boucher
               Telephone: (212) 572-0800
               Telecopier: (212) 755-5263



                                      -8-
<PAGE>   9



               if to the Purchaser, to:

               W-H Investment, L.P.
               c/o The Jordan Company
               767 Fifth Avenue, 48th Floor
               New York, NY 10153
               Attention: Jonathan F. Boucher
               Telephone: (212) 572-0800
               Telecopier: (212) 755-5263

               with a copy to:

               James B. Carlson, Esq.
               Mayer, Brown & Platt
               1675 Broadway
               New York, New York 10019
               Telephone: (212) 506-2515
               Telecopier: (212) 262-1910

Any notice, demand or request so delivered shall constitute valid notice under
this Agreement and shall be deemed to have been received (i) on the day of
actual delivery in the case of personal delivery, (ii) on the next Business Day
after the date when sent in the case of delivery by nationally-recognized
overnight courier, (iii) on the fifth Business Day after the date of deposit in
the U.S. mail in the case of mailing or (iv) upon receipt in the case of a
facsimile transmission. Any party hereto may from time to time by notice in
writing served upon the other as aforesaid designate a different mailing address
or a different Person to which all such notices, demands or requests thereafter
are to be addressed.

         Section 5.2 No Voting Rights; Limitations of Liability. No Warrant
shall entitle the holder thereof to any voting rights or, except as otherwise
provided herein, other rights of a stockholder of the Corporation, as such. No
provision hereof, in the absence of affirmative action by the Holder to purchase
Warrant Shares, and no enumeration herein of the rights or privileges of the
Holder shall give rise to any liability of such Holder for the Exercise Price of
Warrant Shares acquirable by exercise hereof or as a stockholder of the
Corporation.

         Section 5.3 Amendments and Waivers. Any provision of this Agreement may
be amended or waived, but only pursuant to a written agreement signed by the
Corporation and the Holders of a majority of Warrant Shares.

         Section 5.4 Severability. Any provision of this Agreement which is
prohibited or unenforceable in any jurisdiction shall, as to such provision and
such jurisdiction, be ineffective to the extent of such prohibition or
unenforceability without invalidating the remaining provisions of this Agreement
affecting the validity or enforceability of such provision in any other
jurisdiction.

         Section 5.5 Specific Performance. Each Holder shall have the right to
specific performance by the Corporation of the provisions of this Agreement, in
addition to any other


                                      -9-
<PAGE>   10


remedies it may have at law or in equity. The Corporation hereby irrevocably
waives, to the extent that it may do so under applicable law, any defense based
on the adequacy of a remedy at law which may be asserted as a bar to the remedy
of specific performance in any action brought against the Corporation for
specific performance of this Agreement by the Holders of the Warrants or Warrant
Shares.

         Section 5.6 Binding Effect. This Agreement shall be binding upon and
inure to the benefit of the Corporation, each Holder and their respective
successors and assigns.

         Section 5.7 Counterparts. This Agreement may be executed by the parties
hereto in several counterparts, each of which shall be deemed to be an original
and all of which shall constitute together but one and the same agreement. This
Agreement shall become effective when counterparts hereof executed on behalf of
the Corporation and each Holder shall have been received.

         Section 5.8 Governing Law; Entire Agreement. THIS AGREEMENT AND THE
WARRANTS, SHALL EACH BE DEEMED TO BE A CONTRACT MADE UNDER AND GOVERNED BY THE
INTERNAL LAWS OF THE STATE OF NEW YORK. This Agreement and the Warrants,
constitute the entire understanding among the parties hereto with respect to the
subject matter hereof and supersede any prior agreements, written or oral, with
respect thereto.

         Section 5.9 Benefits of this Agreement. Nothing in this Agreement shall
be construed to give to any Person other than the Corporation and each Holder of
a Warrant or a Warrant Share any legal or equitable right, remedy or claim
hereunder.

         Section 5.10 Headings. The various headings of this Agreement are
inserted for convenience only and shall not affect the meaning or interpretation
of this Agreement or any provisions hereof or thereof.

         Section 5.11 Expenses. The Corporation will promptly (and in any event
within thirty (30) days of receiving any statement or invoice therefor) pay all
reasonable fees, expenses and costs relating hereto, including, but not limited
to, (i) the cost of reproducing this Agreement and the Warrants, (ii) the fees
and disbursements of counsel to the Holder in preparing this Agreement, (iii)
all transfer, stamp, documentary or other similar taxes, assessments or charges
levied by any governmental or revenue authority in respect hereof or any other
document referred to herein, (iv) fees and expenses (including, without
limitation, reasonable attorneys' fees) incurred in respect of the enforcement
by Holders of the rights granted to Holders under this Agreement, and (v) the
expenses relating to the consideration, negotiation, preparation or execution of
any amendments, waivers or consents requested by the Corporation pursuant to the
provisions hereof, whether or not any such amendments, waivers or consents are
executed.

         Section 5.12 Attorneys' Fees. In any action or proceeding brought by a
party to enforce any provision of this Agreement, the prevailing party shall be
entitled to recover the reasonable costs and expenses incurred by it in
connection with that action or proceeding (including, but not limited to,
attorneys' fees).



                                      -10-
<PAGE>   11


         Section 5.13 Filings. The Corporation shall, at its own expense,
promptly execute and deliver, or cause to be executed and delivered, to any
holder of Warrants all applications, certificates, instruments and all other
documents and papers that such holder of Warrants may reasonably request in
connection with the obtaining of any consent, approval, qualification, or
authorization of any federal, provincial, state or local government (or any
agency or commission thereof) necessary or appropriate in connection with, or
for the effective exercise of, any Warrants then held by such holder.

         Section 5.14 Other Transactions. Nothing contained herein shall
preclude the Holder from engaging in any transaction, in addition to those
contemplated by this Agreement with the Corporation or any of its Affiliates in
which the Corporation or such Affiliate is not restricted hereby from engaging
with any other Person.

         Section 5.15 Forum Selection and Consent to Jurisdiction. ANY
LITIGATION BASED HEREON, OR ARISING OUT OF, UNDER, OR IN CONNECTION WITH, THIS
AGREEMENT OR ANY COURSE OF CONDUCT, COURSE OF DEALING, STATEMENTS (WHETHER
VERBAL OR WRITTEN) OR ACTIONS OF THE HOLDERS OR THE CORPORATION SHALL BE BROUGHT
AND MAINTAINED EXCLUSIVELY IN THE COURTS OF THE STATE OF NEW YORK OR IN THE
UNITED STATES DISTRICT COURT FOR THE SOUTHERN DISTRICT OF NEW YORK; THE
CORPORATION HEREBY EXPRESSLY AND IRREVOCABLY SUBMITS TO THE JURISDICTION OF THE
COURTS OF THE STATE OF NEW YORK AND OF THE UNITED STATES DISTRICT COURT FOR THE
SOUTHERN DISTRICT OF NEW YORK FOR THE PURPOSE OF ANY SUCH LITIGATION AS SET
FORTH ABOVE AND IRREVOCABLY AGREES TO BE BOUND BY ANY JUDGMENT RENDERED THEREBY
IN CONNECTION WITH SUCH LITIGATION. THE CORPORATION FURTHER IRREVOCABLY CONSENTS
TO THE SERVICE OF PROCESS BY REGISTERED MAIL, POSTAGE PREPAID, OR BY PERSONAL
SERVICE WITHIN OR WITHOUT THE STATE OF NEW YORK. THE CORPORATION HEREBY
EXPRESSLY AND IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY LAW, ANY
OBJECTION WHICH IT MAY HAVE OR HEREAFTER MAY HAVE TO THE LAYING OF VENUE OF ANY
SUCH LITIGATION BROUGHT IN ANY SUCH COURT REFERRED TO ABOVE AND ANY CLAIM THAT
ANY SUCH LITIGATION HAS BEEN BROUGHT IN AN INCONVENIENT FORUM. TO THE EXTENT
THAT THE CORPORATION HAS OR HEREAFTER MAY ACQUIRE ANY IMMUNITY FROM JURISDICTION
OF ANY COURT OF FROM ANY LEGAL PROCESS (WHETHER THROUGH SERVICE OR NOTICE,
ATTACHMENT PRIOR TO JUDGMENT, ATTACHMENT IN AID OF EXECUTION OR OTHERWISE) WITH
RESPECT TO ITSELF OR ITS PROPERTY, THE CORPORATION HEREBY IRREVOCABLY WAIVES
SUCH IMMUNITY IN RESPECT OF ITS OBLIGATIONS UNDER THIS AGREEMENT.

         Section 5.16 Waiver of Jury Trial. THE HOLDERS AND THE CORPORATION
HEREBY KNOWINGLY, VOLUNTARILY AND INTENTIONALLY WAIVE ANY RIGHTS THEY MAY HAVE
TO A TRIAL BY JURY IN RESPECT OF ANY LITIGATION BASED HEREON, OR ARISING OUT OF,
UNDER, OR IN CONNECTION WITH, THIS AGREEMENT, OR ANY COURSE OF CONDUCT,


                                      -11-
<PAGE>   12



COURSE OF DEALING, STATEMENTS (WHETHER VERBAL OR WRITTEN) OR ACTIONS OF THE
HOLDERS OR THE CORPORATION. THE CORPORATION ACKNOWLEDGES AND AGREES THAT IT HAS
RECEIVED FULL AND SUFFICIENT CONSIDERATION FOR THIS PROVISION AND THAT THIS
PROVISION IS A MATERIAL INDUCEMENT FOR THE HOLDERS ENTERING INTO THIS AGREEMENT.

         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed and delivered by their authorized officers, all as of the date and
year first above written.

                                                 W-H ENERGY SERVICES, INC.

                                                 By: /s/ Kenneth T. White, Jr.
                                                     --------------------------
                                                 Name:
                                                 Title:

ATTEST:

By:
   --------------------------------------
Name:
Title:





                                      -12-
<PAGE>   13


                                                                         ANNEX 1

                            ELECTION TO EXERCISE FORM

                 (To Be Executed By The Holders of This Warrant

                       In Order to Exercise This Warrant)

         The undersigned hereby irrevocably elects to exercise the right to
purchase shares of Class A Common Stock of W-H Energy Services, Inc. covered by
this Warrant according to the conditions hereof and herewith makes payment of
the Exercise Price of such shares in full.



                                      ------------------------------------------
                                      Signature


                                      ------------------------------------------

                                      ------------------------------------------
                                      Address

Dated:
      -----------------------------




                                Annex 1 - Page 1
<PAGE>   14


                                                                         ANNEX 2

                                 ASSIGNMENT FORM

                  (To Be Executed By The Holder of This Warrant

                  In Order to Assign This Warrant Certificate)

         FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers
unto ___________________ this Warrant and all rights evidenced thereby and does
irrevocably constitute and appoint ________________, attorney, to transfer the
said Warrant on the books of the Corporation.


                                      ------------------------------------------
                                      Signature


                                      ------------------------------------------

                                      ------------------------------------------
                                      Address

Dated:
      -----------------------------







                               Annex 2 - Page - 1
<PAGE>   15


                                                                         ANNEX 3

                                  EXCHANGE FORM

                  (To Be Executed By The Holder of This Warrant

                  In Order to Assign This Warrant Certificate)

         The undersigned hereby irrevocably elects to exchange this Warrant to
purchase _______ shares of Class A Common Stock of W-H Energy Services, Inc.
covered by this Warrant for ________ Warrants to purchase the denominations of
shares of Class A Common Stock set forth below to the persons named and hereby
sells, assigns and transfers unto such persons that portion of this Warrant
represented by such new Warrants and all rights evidenced thereby and does
irrevocably constitute and appoint attorney, to exchange and transfer this
Warrant as aforesaid on the books of the Corporation.

Number of Warrant Shares                        Assignee


---------------------------------               --------------------------------

---------------------------------               --------------------------------



                                                --------------------------------
                                                Signature


                                                --------------------------------

                                                --------------------------------
                                                Address

FOR USE BY THE CORPORATION ONLY:

This Warrant No. _____ canceled (or transferred or exchanged) this _____ day of
________, _____ shares of Class A Common Stock issued therefor in the name of
__________, Warrant No. _____ for _______ shares of Class A Common Stock in the
name of __________________.



Dated:
      ----------------------------






                                Annex 3 - Page 1