<PAGE>

                                                                     EXHIBIT 3.1

                                    SECOND

                             AMENDED AND RESTATED

                                    BYLAWS

                                      OF

                                TUBOSCOPE INC.


                        As Adopted by Board Resolution
                                 May 13, 1999
<PAGE>

                                    SECOND

                             AMENDED AND RESTATED

                                    BYLAWS

                                      OF

                                TUBOSCOPE INC.


                               TABLE OF CONTENTS
                               -----------------

<TABLE>
<CAPTION>
                                                                            Page
                                                                            ----
<S>                                                                         <C>
ARTICLE I.      OFFICES....................................................  1

    Section 1.  Principal Office...........................................  1
    Section 2.  Other Offices..............................................  1

ARTICLE II.     MEETINGS OF STOCKHOLDERS...................................  1

    Section 1.  Place of Meetings..........................................  1
    Section 2.  Annual Meetings............................................  1
    Section 3.  Quorum.....................................................  1
    Section 4.  Voting.....................................................  2
    Section 5.  Proxies....................................................  2
    Section 6.  Special Meetings...........................................  2
    Section 7.  Notice of Meeting..........................................  2
    Section 8.  List of Stockholders.......................................  2

ARTICLE III.    DIRECTORS..................................................  3

    Section 1.  Number and Term of Office of Directors.....................  3
    Section 2.  Vacancies..................................................  3
    Section 3.  Powers.....................................................  3
    Section 4.  Meetings, Offices and Books Outside the State of
                Delaware...................................................  3
    Section 5.  Regular Meetings...........................................  4
    Section 6.  Special Meetings...........................................  4
    Section 7.  Quorum.....................................................  4
    Section 8.  Action by Unanimous Written Consent Without a Meeting......  4
    Section 9.  Telephonic Meetings........................................  4
    Section 10. Committees of Directors....................................  4
</TABLE>

                                       i
<PAGE>

<TABLE>
<S>                                                                         <C>
   Section 11.  Meetings of Committees....................................   5
   Section 12.  Compensation..............................................   5
   Section 13.  Indemnification...........................................   5

ARTICLE IV. OFFICERS......................................................   8

   Section 1.   Officers..................................................   8
   Section 2.   Election..................................................   8
   Section 3.   Subordinate Officers......................................   8
   Section 4.   Salaries..................................................   8
   Section 5.   Term of Office............................................   8
   Section 6.   Chairman of the Board.....................................   8
   Section 7.A  Chief Executive Officer...................................   8
   Section 7.B  President.................................................   9
   Section 8.   Vice Presidents...........................................   9
   Section 9.   Secretary.................................................   9
   Section 10.  Assistant Secretary.......................................   9
   Section 11.  Treasurer.................................................   9
   Section 12.  Assistant Treasurer.......................................  10

ARTICLE V. STOCK..........................................................  10

   Section 1.   Certificates..............................................  10
   Section 2.   Signatures................................................  10
   Section 3.   Rights and Preferences....................................  10
   Section 4.   Lost, Stolen or Destroyed Certificates....................  10
   Section 5.   Transfers.................................................  11
   Section 6.   Record Date...............................................  11
   Section 7.   Registered Stockholders...................................  11
   Section 8.   Declaration and Payment of Dividends......................  11
   Section 9.   Reserve Fund..............................................  11

ARTICLE VI.GENERAL PROVISIONS.............................................  12

   Section 1.   Checks....................................................  12
   Section 2.   Fiscal Year...............................................  12
   Section 3.   Corporate Seal............................................  12
   Section 4.   Notices...................................................  12
   Section 5.   Waiver of Notice..........................................  12
   Section 6.   Annual Statement..........................................  12

ARTICLE VII     AMENDMENTS................................................  12
</TABLE>

                                      ii
<PAGE>

                                    SECOND
                             AMENDED AND RESTATED
                                    BYLAWS
                                      OF
                                TUBOSCOPE INC.


                                  ARTICLE I.

                                    OFFICES
                                    -------


          Section 1.  Principal Office. The registered office shall be in the
                      -----------------
City of Wilmington, County of New Castle, State of Delaware.

          Section 2.  Other Offices. The corporation may also have offices at
                      -------------
such other places both within and outside the State of Delaware as the Board of
Directors may from time to time determine or the business of the corporation may
require.

                                  ARTICLE II.

                           MEETINGS OF STOCKHOLDERS
                           ------------------------

          Section 1.  Place of Meetings.  Meetings of stockholders shall be held
                      -----------------
at any place within or outside the State of Delaware designated by the Board of
Directors. In the absence of any such designation, stockholders' meetings shall
be held at the principal executive office of the corporation.

          Section 2.  Annual Meetings. The annual meeting of stockholders shall
                      ---------------
be held each year on a date and a time designated by the Board of Directors. At
each annual meeting directors shall be elected and any other proper business may
be transacted.

          Section 3.  Quorum. A majority of the stock issued and outstanding and
                      ------
entitled to vote at any meeting of stockholders, the holders of which are
present in person or represented by proxy, shall constitute a quorum for the
transaction of business except as otherwise provided by law, by the Certificate
of Incorporation, or by these Bylaws. A quorum, once established, shall not be
broken by the withdrawal of enough votes to leave less than a quorum and the
votes present may continue to transact business until adjournment. If, however,
such quorum shall not be present or represented at any meeting of the
stockholders, a majority of the voting stock represented in person or by proxy
may adjourn the meeting from time to time, without notice other than
announcement at the meeting, until a quorum shall be present or represented. At
such adjourned meeting at which a quorum shall be present or represented, any
business may be transacted which might have been transacted at the meeting as
originally notified. If the adjournment is for more than thirty days, or if
after the adjournment a new record date is fixed for the adjourned meeting, a
notice of the adjourned meeting shall be given to each stockholder of record
entitled to vote thereat.

                                       1
<PAGE>

          Section 4.  Voting.  When a quorum is present at any meeting the vote
                      ------
of the holders of a majority of the stock having voting power present in person
or represented by proxy shall decide any question brought before such meeting,
unless the question is one upon which by express provision of statute, or the
Certificate of Incorporation, or these Bylaws, a different vote is required in
which case such express provision shall govern and control the decision of such
question. Directors shall be elected by a plurality of the votes of the shares
present in person or represented by proxy at the meeting and entitled to vote on
the election of directors. Each stockholder shall have one vote for each share
of stock having voting power, registered in his name on the books of the
corporation on the record date set by the Board of Directors as provided in
Article V, Section 6 hereof.

          Section 5.  Proxies.  At each meeting of the stockholders, each
                      -------
stockholder having the right to vote may vote in person or may authorize another
person or persons to act for him by proxy appointed by an instrument in writing
executed by such stockholder and bearing a date not more than three years prior
to said meeting, unless said instrument provides for a longer period. All
proxies must be filed with the Secretary of the corporation at the beginning of
each meeting in order to be counted in any vote at the meeting.

          Section 6.  Special Meetings.  Special meetings of the stockholders,
                      ----------------
for any purpose or purposes, unless otherwise prescribed by statute or by the
Certificate of Incorporation, may be called by the President and shall be called
by the President or the Secretary at the request in writing of a majority of the
Board of Directors, or at the request in writing of stockholders owning a
majority in amount of the entire capital stock of the corporation issued and
outstanding, and entitled to vote. Such request shall state the purpose or
purposes of the proposed meeting. Business transacted at any special meeting of
stockholders shall be limited to the purposes stated in the notice.

          Section 7.  Notice of Meeting.  Whenever stockholders are required or
                      -----------------
permitted to take any action at a meeting, a written notice of the meeting shall
be given which notice shall state the place, date and hour of the meeting, and,
in the case of a special meeting, the purpose or purposes for which the meeting
is called. The written notice of any meeting shall be given to each stockholder
entitled to vote at such meeting not less than ten nor more than sixty days
before the date of the meeting. If mailed, notice is given when deposited in the
United States mail, postage prepaid, directed to the stockholder at his address
as it appears on the records of the corporation.

          Section 8.  List of Stockholders.  The officer who has charge of the
                      --------------------
stock ledger of the corporation shall prepare and make, at least ten days before
every meeting of stockholders, a complete list of the stockholders entitled to
vote at the meeting, arranged in alphabetical order, and showing the address of
each stockholder and the number of shares registered in the name of each
stockholder. Such list shall be open to the examination of any stockholder, for
any purpose germane to the meeting, during ordinary business hours, for a period
of at least ten days prior to the meeting, either at a place within the city
where the meeting is to be held, which place shall be specified in the notice of
the meeting, or, if not so specified, at the place where the meeting is to be
held. The list shall also be produced and kept at the time

                                       2
<PAGE>

and place of the meeting during the whole time thereof, and may be inspected by
any stockholder who is present.

                                 ARTICLE III.

                                   DIRECTORS
                                   ---------

          Section 1.  Number and Term of Office of Directors.  The number of
                      --------------------------------------
directors which shall constitute the whole Board shall be not less than one (1)
nor more than ten (10). The Board shall be fixed from time to time, within the
limits specified above, by a duly adopted resolution of the Board or the
stockholders in accordance with the Certificate of Incorporation. The directors
need not be stockholders. The directors shall be elected at the annual meeting
of the stockholders, except as provided in Section 2 of this Article, and each
director elected shall hold office until his successor is elected and qualified,
or until his earlier resignation or removal. Any director may resign at any time
upon written notice to the corporation. Any director or the entire Board of
Directors may be removed from the Board of Directors at any meeting of
stockholders but only for cause and only by the affirmative vote of holders of
at least 66 2/3% of the outstanding shares of the common stock of the
corporation entitled to vote.

          Section 2.  Vacancies.  Vacancies on the Board of Directors by reason
                      ---------
of death, resignation, retirement, disqualification, removal from office, or
otherwise, and newly created directorships resulting from any increase in the
authorized number of directors shall be filled only by a majority of the
directors then in office, although less than a quorum, or by a sole remaining
director. Any director so chosen shall hold office until the next annual
election of directors and until his successor is duly elected and qualified, or
until his earlier resignation or removal. If there are no directors in office,
then an election of directors may be held in the manner provided by statute. If,
at the time of filling any vacancy or any newly created directorship, the
directors then in office shall constitute less than a majority of the whole
Board (as constituted immediately prior to any such increase), the Court of
Chancery may, upon application of any stockholder or stockholders holding at
least ten percent of the total number of the shares at the time outstanding
having the right to vote for such directors, summarily order an election to be
held to fill any such vacancies or newly created directorships, or to replace
the directors chosen by the directors then in office.

          Section 3.  Powers.  The property, business and affairs of the
                      ------
corporation shall be managed by or under the direction of its Board of
Directors. In addition to the powers and authorities by these Bylaws expressly
conferred upon them, the Board may exercise all such powers of the corporation
and do all such lawful acts and things as are not by statute or by the
Certificate of Incorporation or by these Bylaws directed or required to be
exercised or done by the stockholders.

          Section 4.  Meetings, Offices and Books Outside the State of Delaware.
                      ---------------------------------------------------------
The directors may hold their meetings and have one or more offices, and keep the
books of the corporation outside of the State of Delaware.

                                       3
<PAGE>

          Section 5.  Regular Meetings.  Regular meetings of the Board of
                      ----------------
Directors or of any committee thereof may be held without notice at such time
and place as shall from time to time be determined by the Board.

          Section 6.  Special Meetings.  Special meetings of the Board of
                      ----------------
Directors for any purpose or purposes may be called at any time by the Chairman
of the Board or the President or in like manner by the President or the
Secretary upon the written request of any two directors.

          Notice of the time and place of special meetings shall be delivered
personally or by telephone to each director or sent by first-class mail, by
facsimile or by telegram, charges prepaid, addressed to each director at his or
her address as it is shown upon the records of the corporation.  In case such
notice is mailed, it shall be deposited in the United States mail at least four
(4) days prior to the time of the holding of the meeting.  In case such notice
is delivered personally, or by telephone, facsimile or telegram, it shall be
delivered personally or by telephone, facsimile or to the telegraph company at
least forty-eight (48) hours prior to the time of the holding of the meeting.
Any oral notice given personally or by telephone may be communicated to either
the director or to a person at the office of the director who the person giving
the notice has reason to believe will promptly communicate it to the director.
The notice need not specify the purpose of the meeting nor the place if the
meeting is to be held at the principal executive office of the corporation.

          Section 7.  Quorum.  At all meetings of the Board of Directors a
                      ------
majority of the authorized number of directors shall be necessary and sufficient
to constitute a quorum for the transaction of business, and the vote of a
majority of the directors present at any meeting at which there is a quorum,
shall be the act of the Board of Directors, except as may be otherwise
specifically provided by statute, by the Certificate of Incorporation or by
these Bylaws. If a quorum shall not be present at any meeting of the Board of
Directors, the directors present thereat may adjourn the meeting from time to
time, without notice other than announcement at the meeting, until a quorum is
present.

          Section 8.  Action by Unanimous Written Consent Without a Meeting.
                      -----------------------------------------------------
Unless otherwise restricted by the Certificate of Incorporation or these Bylaws,
any action required or permitted to be taken at any meeting of the Board of
Directors or of any committee thereof may be taken without a meeting, if all
members of the Board or committee, as the case may be, consent thereto in
writing, and the writing or writings are filed with the minutes of proceedings
of the Board or committee.

          Section 9.  Telephonic Meetings.  Unless otherwise restricted by the
                      -------------------
Certificate of Incorporation or these Bylaws, members of the Board of Directors,
or any committee designated by the Board of Directors, may participate in a
meeting of the Board of Directors, or any committee, by means of conference
telephone or similar communications equipment by means of which all persons
participating in the meeting can hear each other, and such participation in a
meeting shall constitute presence in person at such meeting.

          Section 10. Committees of Directors.  The Board of Directors may, by
                      -----------------------
resolution passed by a majority of the whole Board, designate one or more
committees, each

                                       4
<PAGE>

such committee to consist of one or more of the directors of the corporation.
The Board may designate one or more directors as alternate members of any
committee, who may replace any absent or disqualified member at any meeting of
the committee. In the absence or disqualification of a member of a committee,
the member or members thereof present at any meeting and not disqualified from
voting, whether or not he or they constitute a quorum, may unanimously appoint
another member of the Board of Directors to act at the meeting in the place of
any such absent or disqualified member. Any such committee, to the extent
provided in the resolution of the Board of Directors, shall have and may
exercise all the powers and authority of the Board of Directors in the
management of the business and affairs of the corporation, and may authorize the
seal of the corporation to be affixed to all papers which may require it; but no
such committee shall have the power or authority in reference to amending the
Certificate of Incorporation (except as provided by statute), adopting an
agreement of merger or consolidation, recommending to the stockholders the sale,
lease or exchange of all or substantially all of the corporation's property and
assets, recommending to the stockholders a dissolution of the corporation or a
revocation of a dissolution, or amending the Bylaws of the corporation; and,
unless the resolution or the Certificate of Incorporation expressly so provide,
no such committee shall have the power or authority to declare a dividend, to
authorize the issuance of stock or to adopt a certificate of ownership and
merger.

          Section 11.  Meetings of Committees.  Each committee shall keep
                       ----------------------
regular minutes of its meetings and report the same to the Board of Directors
when required.

          Section 12.  Compensation.  Unless otherwise restricted by the
                       ------------
Certificate of Incorporation or these Bylaws, the Board of Directors shall have
the authority to fix the compensation of directors. The directors may be paid
their expenses, if any, of attendance at each meeting of the Board of Directors
and may be paid a fixed sum for attendance at each meeting of the Board of
Directors or a stated salary as director. No such payment shall preclude any
director from serving the corporation in any other capacity and receiving
compensation therefor. Members of special or standing committees may be allowed
like compensation for attending committee meetings.

                                INDEMNIFICATION
                                ---------------

          Section 13.  Indemnification.
                       ---------------

          (a) The corporation shall indemnify any person who was or is a party
or is threatened to be made a party to any threatened, pending or completed
action, suit or proceeding, whether civil, criminal, administrative or
investigative (other than an action by or in the right of the corporation) by
reason of the fact that he is or was a director, officer, employee or agent of
the corporation, or is or was serving at the request of the corporation as a
director, officer, employee or agent of another corporation, partnership, joint
venture, trust or other enterprise, against expenses (including attorneys'
fees), judgments, fines and amounts paid in settlement actually and reasonably
incurred by him in connection with such action, suit or proceeding if he acted
in good faith and in a manner he reasonably believed to be in or not opposed to
the best interests of the corporation, and, with respect to any criminal action
or proceeding, had no

                                       5
<PAGE>

reasonable cause to believe his conduct was unlawful. The termination of any
action, suit or proceeding by judgment, order, settlement, conviction, or upon a
plea of nolo contendere or its equivalent, shall not, of itself, create a
presumption that the person did not act in good faith and in a manner which he
reasonably believed to be in or not opposed to the best interests of the
corporation, and, with respect to any criminal action or proceeding, had
reasonable cause to believe that his conduct was unlawful.

          (b) The corporation shall indemnify any person who was or is a party
or is threatened to be made a party to any threatened, pending or completed
action or suit by or in the right of the corporation to procure a judgment in
its favor by reason of the fact that he is or was a director, officer, employee
or agent of the corporation, or is or was serving at the request of the
corporation as a director, officer, employee or agent of another corporation,
partnership, joint venture, trust or other enterprise against expenses
(including attorneys' fees) actually and reasonably incurred by him in
connection with the defense or settlement of such action or suit if he acted in
good faith and in a manner he reasonably believed to be in or not opposed to the
best interests of the corporation and except that no such indemnification shall
be made in respect of any claim, issue or matter as to which such person shall
have been adjudged to be liable to the corporation unless and only to the extent
that the Court of Chancery of Delaware or the court in which such action or suit
was brought shall determine upon application that, despite the adjudication of
liability but in view of all the circumstances of the case, such person is
fairly and reasonably entitled to indemnity for such expenses which such Court
of Chancery or such other court shall deem proper.

          (c) To the extent that a director, officer, employee or agent of the
corporation shall be successful on the merits or otherwise in defense of any
action, suit or proceeding referred to in paragraphs (a) and (b), or in defense
of any claim, issue or matter therein, he shall be indemnified against expenses
(including attorneys' fees) actually and reasonably incurred by him in
connection therewith.

          (d) Any indemnification under paragraphs (a) and (b) (unless ordered
by a court) shall be made by the corporation only as authorized in the specific
case upon a determination that indemnification of the director, officer,
employee or agent is proper in the circumstances because he has met the
applicable standard of conduct set forth in paragraphs (a) and (b).  Such
determination shall be made (1) by the Board of Directors by a majority vote of
a quorum consisting of directors who were not parties to such action, suit or
proceeding, or (2) if such a quorum is not obtainable, or, even if obtainable a
quorum of disinterested directors so directs, by independent legal counsel in a
written opinion, or (3) by the stockholders.

          (e) Expenses incurred in defending a civil or criminal action, suit or
proceeding may be paid by the corporation in advance of the final disposition of
such action, suit or proceeding upon receipt of an undertaking by or on behalf
of the director, officer, employee or agent to repay such amount if it shall
ultimately be determined that he is not entitled to be indemnified by the
corporation as authorized in this Section 13.

                                       6
<PAGE>

          (f) The indemnification and advancement of expenses provided by, or
granted pursuant to, the other subsections of this Section 13 shall not be
deemed exclusive of any other rights to which those seeking indemnification or
advancement of expenses may be entitled under any bylaw, agreement, vote of
stockholders or disinterested directors or otherwise, both as to action in his
official capacity and as to action in another capacity while holding such
office.

          (g) The Board of Directors may authorize, by a vote of a majority of a
quorum of the Board of Directors, the corporation to purchase and maintain
insurance on behalf of any person who is or was a director, officer, employee or
agent of the corporation, or is or was serving at the request of the corporation
as a director, officer, employee or agent of another corporation, partnership,
joint venture, trust or other enterprise against any liability asserted against
him and incurred by him in any such capacity, or arising out of his status as
such, whether or not the corporation would have the power to indemnify him
against such liability under the provisions of this Section 13.

          (h) For the purposes of this Section 13, references to "the
corporation" shall include, in addition to the resulting corporation, any
constituent corporation (including any constituent of a constituent) absorbed in
a consolidation or merger which, if its separate existence had continued, would
have had power and authority to indemnify its directors, officers, and employees
or agents, so that any person who is or was a director, officer, employee or
agent of such constituent corporation, or is or was serving at the request of
such constituent corporation as a director, officer, employee or agent of
another corporation, partnership, joint venture, trust or other enterprise,
shall stand in the same position under the provisions of this Section with
respect to the resulting or surviving corporation as he would have with respect
to such constituent corporation if its separate existence had continued.

          (i) For purposes of this section, references to "other enterprises"
shall include employee benefit plans; references to "fines" shall include any
excise taxes assessed on a person with respect to an employee benefit plan; and
references to "serving at the request of the corporation" shall include service
as a director, officer, employee or agent of the corporation which imposes
duties on, or involves services by, such director, officer, employee or agent
with respect to an employee benefit plan, its participants or beneficiaries; and
a person who acted in good faith and in a manner he reasonably believed to be in
the interest of the participants and beneficiaries of an employee benefit plan
shall be deemed to have acted in a manner "not opposed to the best interests of
the corporation" as referred to in this section.

          (j) The indemnification and advancement of expenses provided by, or
granted pursuant to, this section shall, unless otherwise provided when
authorized or ratified, continue as to a person who has ceased to be a director,
officer, employee or agent and shall inure to the benefit of the heirs,
executors and administrators of such a person.

                                       7
<PAGE>

                                  ARTICLE IV.

                                   OFFICERS
                                   --------

          Section 1.  Officers.  The officers of this corporation shall be
                      --------
chosen by the Board of Directors and shall include a President, a Secretary, and
a Treasurer. The corporation may also have at the discretion of the Board of
Directors such other officers as are desired, including one or more Vice
Presidents, one or more Assistant Secretaries and Assistant Treasurers, and such
other officers as may be appointed in accordance with the provisions of Section
3 hereof. The corporation may also have at the discretion of the Board of
Directors a Chairman of the Board. In the event there are two or more Vice
Presidents, then one or more may be designated as Executive Vice President,
Senior Vice President, or other similar or dissimilar title. At the time of the
election of officers, the directors may by resolution determine the order of
their rank. Any number of offices may be held by the same person, unless the
Certificate of Incorporation or these Bylaws otherwise provide.

          Section 2.  Election.  The Board of Directors, at its first meeting
                      --------
after each annual meeting of stockholders, shall choose the officers of the
corporation.

          Section 3.  Subordinate Officers.  The Board of Directors may appoint
                      --------------------
such other officers and agents as it shall deem necessary who shall hold their
offices for such terms and shall exercise such powers and perform such duties as
shall be determined from time to time by the Board.

          Section 4.  Salaries.  The salaries of all officers and agents of the
                      --------
corporation shall be fixed by the Board of Directors.

          Section 5.  Term of Office.  The officers of the corporation shall
                      --------------
hold office until their successors are chosen and qualify in their stead. Any
officer elected or appointed by the Board of Directors may be removed at any
time by the affirmative vote of a majority of the Board of Directors. If the
office of any officer or officers becomes vacant for any reason, the vacancy
shall be filled by the Board of Directors.

          Section 6.  Chairman of the Board.  The Chairman of the Board, if
                      ---------------------
elected, shall, if present, preside at all meetings of the Board of Directors
and exercise and perform such other powers and duties as may be from time to
time assigned to him by the Board of Directors or prescribed by these Bylaws. If
there is no Chief Executive Officer or President, the Chairman of the Board
shall, in addition, be the Chief Executive Officer of the corporation and shall
have the powers and duties prescribed in Section 7A of this Article IV.

          Section 7A. Chief Executive Officer.  Subject to such supervisory
                      -----------------------
powers, if any, as may be given by the Board of Directors to the Chairman of the
Board, if there be such an officer, the Chief Executive Officer shall, subject
to the control of the Board of Directors, have general supervision, direction
and control of the business and officers of the corporation. He shall be an
ex-officio member of all committees and shall have the general powers and duties
of management usually vested in the office of Chief Executive Officer of
corporations, and shall

                                       8
<PAGE>

have such other powers and duties as may be prescribed by the Board of Directors
or these Bylaws.

          Section 7B. President.  In the absence or disability of the Chief
                      ---------
Executive Officer, if there be such an officer, the President shall perform all
the duties of the Chief Executive Officer, and when so acting shall have all the
powers of and be subject to all the restrictions upon the Chief Executive
Officer. The President shall have such other duties as from time to time may be
prescribed for him by the Board of Directors or the Chief Executive Officer.

          Section 8.  Vice Presidents.  In the absence or disability of the
                      ---------------
President, the Vice Presidents in order of their rank as fixed by the Board of
Directors, or if not ranked, the Vice President designated by the Board of
Directors, shall perform all the duties of the President, and when so acting
shall have all the powers of and be subject to all the restrictions upon the
President. The Vice Presidents shall have such other duties as from time to time
may be prescribed for them, respectively, by the Board of Directors.

          Section 9.  Secretary.  The Secretary shall attend all sessions of the
                      ---------
Board of Directors and all meetings of the stockholders and record all votes and
the minutes of all proceedings in a book to be kept for that purpose; and shall
perform like duties for the standing committees when required by the Board of
Directors. He shall give, or cause to be given, notice of all meetings of the
stockholders and of the Board of Directors, and shall perform such other duties
as may be prescribed by the Board of Directors or these Bylaws. He shall keep in
safe custody the seal of the corporation, and when authorized by the Board,
affix the same to any instrument requiring it, and when so affixed it shall be
attested by his signature or by the signature of an Assistant Secretary. The
Board of Directors may give general authority to any other officer to affix the
seal of the corporation and to attest the affixing by his signature.

          Section 10. Assistant Secretary.  The Assistant Secretary, or if there
                      -------------------
be more than one, the Assistant Secretaries in the order determined by the Board
of Directors, or if there be no such determination, the Assistant Secretary
designated by the Board of Directors, shall, in the absence or disability of the
Secretary, perform the duties and exercise the powers of the Secretary and shall
perform such other duties and have such other powers as the Board of Directors
may from time to time prescribe.

          Section 11.  Treasurer.  The Treasurer shall have the custody of the
                       ---------
corporate funds and securities and shall keep full and accurate accounts of
receipts and disbursements in books belonging to the corporation and shall
deposit all moneys, and other valuable effects in the name and to the credit of
the corporation, in such depositories as may be designated by the Board of
Directors. He shall disburse the funds of the corporation as may be ordered by
the Board of Directors, taking proper vouchers for such disbursements, and shall
render to the Board of Directors, at its regular meetings, or when the Board of
Directors so requires, an account of all his transactions as Treasurer and of
the financial condition of the corporation. If required by the Board of
Directors, he shall give the corporation a bond, in such sum and with such
surety or sureties as shall be satisfactory to the Board of Directors, for the
faithful performance of the duties of his office and for the restoration to the
corporation, in case of his death, resignation,

                                       9
<PAGE>

retirement or removal from office, of all books, papers, vouchers, money and
other property of whatever kind in his possession or under his control belonging
to the corporation.

          Section 12.  Assistant Treasurer.  The Assistant Treasurer, or if
                       -------------------
there shall be more than one, the Assistant Treasurers in the order determined
by the Board of Directors, or if there be no such determination, the Assistant
Treasurer designated by the Board of Directors, shall, in the absence or
disability of the Treasurer, perform the duties and exercise the powers of the
Treasurer and shall perform such other duties and have such other powers as the
Board of Directors may from time to time prescribe.

                                  ARTICLE V.

                                     STOCK
                                     -----

          Section 1.  Certificates.  Every holder of stock of the corporation
                      ------------
shall be entitled to have a certificate signed by, or in the name of the
corporation by, the Chairman or Vice Chairman of the Board of Directors, or the
President or a Vice President, and by the Secretary or an Assistant Secretary,
or the Treasurer or an Assistant Treasurer of the corporation, certifying the
number of shares represented by the certificate owned by such stockholder in the
corporation.

          Section 2.  Signatures.  Any or all of the signatures on the
                      ----------
certificate may be a facsimile. In case any officer, transfer agent, or
registrar who has signed or whose facsimile signature has been placed upon a
certificate shall have ceased to be such officer, transfer agent, or registrar
before such certificate is issued, it may be issued by the corporation with the
same effect as if he were such officer, transfer agent, or registrar at the date
of issue.

          Section 3.  Rights and Preferences.  If the corporation shall be
                      ----------------------
authorized to issue more than one class of stock or more than one series of any
class, the powers, designations, preferences and relative, participating,
optional or other special rights of each class of stock or series thereof and
the qualification, limitations or restrictions of such preferences and/or rights
shall be set forth in full or summarized on the face or back of the certificate
which the corporation shall issue to represent such class or series of stock,
provided that, except as otherwise provided in section 202 of the General
Corporation Law of Delaware, in lieu of the foregoing requirements, there may be
set forth on the face or back of the certificate which the corporation shall
issue to represent such class or series of stock, a statement that the
corporation will furnish without charge to each stockholder who so requests the
powers, designations, preferences and relative, participating, optional or other
special rights of each class of stock or series thereof and the qualifications,
limitations or restrictions of such preferences and/or rights.

          Section 4.  Lost, Stolen or Destroyed Certificates.  The Board of
                      --------------------------------------
Directors may direct a new certificate or certificates to be issued in place of
any certificate or certificates theretofore issued by the corporation alleged to
have been lost, stolen or destroyed, upon the making of an affidavit of that
fact by the person claiming the certificate of stock to be lost, stolen or
destroyed. When authorizing such issue of a new certificate or certificates, the
Board of

                                       10
<PAGE>

Directors may, in its discretion and as a condition precedent to the issuance
thereof, require the owner of such lost, stolen or destroyed certificate or
certificates, or his legal representative, to advertise the same in such manner
as it shall require and/or to give the corporation a bond in such sum as it may
direct as indemnity against any claim that may be made against the corporation
with respect to the certificate alleged to have been lost, stolen or destroyed.

          Section 5.  Transfers.  Upon surrender to the corporation, or the
                      ---------
transfer agent of the corporation, of a certificate for shares duly endorsed or
accompanied by proper evidence of succession, assignation or authority to
transfer, it shall be the duty of the corporation to issue a new certificate to
the person entitled thereto, cancel the old certificate and record the
transaction upon its books.

          Section 6.  Record Date.  In order that the corporation may determine
                      -----------
the stockholders entitled to notice of or to vote at any meeting of the
stockholders, or any adjournment thereof, or to express consent to corporate
action in writing without a meeting, or entitled to receive payment of any
dividend or other distribution or allotment of any rights, or entitled to
exercise any rights in respect of any change, conversion or exchange of stock or
for the purpose of any other lawful action, the Board of Directors may fix a
record date which shall not precede the date upon which the resolution fixing
the record date is adopted and which shall not be more than sixty nor less than
ten days before the date of such meeting, nor more than sixty days prior to any
other action. A determination of stockholders of record entitled to notice of or
to vote at a meeting of stockholders shall apply to any adjournment of the
meeting; provided, however, that the Board of Directors may fix a new record
date for the adjourned meeting.

          Section 7.  Registered Stockholders.  The corporation shall be
                      -----------------------
entitled to treat the holder of record of any share or shares of stock as the
holder in fact thereof and accordingly shall not be bound to recognize any
equitable or other claim or interest in such share on the part of any other
person, whether or not it shall have express or other notice thereof, except as
expressly provided by the laws of the State of Delaware.

          Section 8.  Declaration and Payment of Dividends.  Dividends upon the
                      ------------------------------------
capital stock of the corporation, subject to the provisions of the Certificate
of Incorporation, if any, may be declared by the Board of Directors at any
regular or special meeting, pursuant to law. Dividends may be paid in cash, in
property, or in shares of the capital stock, subject to the provisions of the
Certificate of Incorporation.

          Section 9.  Reserve Fund.  Before payment of any dividend there may be
                      ------------
set aside out of any funds of the corporation available for dividends such sum
or sums as the directors from time to time, in their absolute discretion, think
proper as a reserve fund to meet contingencies, or for equalizing dividends, or
for repairing or maintaining any property of the corporation, or for such other
purpose as the directors shall think conducive to the interests of the
corporation, and the directors may abolish any such reserve.

                                       11
<PAGE>

                                  ARTICLE VI.

                              GENERAL PROVISIONS
                              ------------------

          Section 1.  Checks.  All checks or demands for money and notes of the
                      ------
corporation shall be signed by such officer or officers as the Board of
Directors may from time to time designate.

          Section 2.  Fiscal Year.  The fiscal year of the corporation shall be
                      -----------
fixed by resolution of the Board of Directors.

          Section 3.  Corporate Seal.  The corporate seal shall have inscribed
                      --------------
thereon the name of the corporation, the year of its organization and the words
"Corporate Seal, Delaware". Said seal may be used by causing it or a facsimile
thereof to be impressed or affixed or reproduced or otherwise.

          Section 4.  Notices.  Whenever, under the provisions of the statutes
                      -------
or of the Certificate of Incorporation or of these Bylaws, notice is required to
be given to any director or stockholder, it shall not be construed to mean
personal notice, but such notice may be given in writing, by mail, addressed to
such director or stockholder, at his address as it appears on the records of the
corporation, with postage thereon prepaid, and such notice shall be deemed to be
given at the time when the same shall be deposited in the United States mail.
Notice to directors may also be given by facsimile, telegram and telephone.

          Section 5.  Waiver of Notice.  Whenever any notice is required to be
                      ----------------
given under the provisions of the statutes or of the Certificate of
Incorporation or of these Bylaws, a waiver thereof in writing, signed by the
person or persons entitled to said notice, whether before or after the time
stated therein, shall be deemed equivalent thereto.

          Section 6.  Annual Statement.  The Board of Directors shall present at
                      ----------------
each annual meeting, and at any special meeting of the stockholders when called
for by vote of the stockholders, a full and clear statement of the business and
condition of the corporation.

                                 ARTICLE VII.

                                  AMENDMENTS
                                  ----------

          These Bylaws may be altered, amended or repealed or new Bylaws may be
adopted by the stockholders or by the Board of Directors, when such power is
conferred upon the Board of Directors by the Certificate of Incorporation, at
any regular meeting of the stockholders or of the Board of Directors or at any
special meeting of the stockholders or of the Board of Directors if notice of
such alteration, amendment, repeal or adoption of new Bylaws be contained in the
notice of such special meeting.  If the power to adopt, amend or repeal Bylaws
is conferred upon the Board of Directors by the Certificate of Incorporation it
shall not divest or limit the power of the stockholders to adopt, amend or
repeal Bylaws.

                                       12
<PAGE>

                           CERTIFICATE OF SECRETARY
                           ------------------------

          I, the undersigned, do hereby certify:

          (1)  That I am the duly elected and acting Vice President, Secretary
and General Counsel of Tuboscope Inc., a Delaware corporation; and

          (2)  That the foregoing Second Amended and Restated Bylaws constitute
the bylaws of said corporation as duly adopted by the Board of Directors on May
13, 1999.


          IN WITNESS WHEREOF, I have hereunto subscribed my name this 13th day
of May, 1999.



                              /s/ JAMES F. MARONEY, III
                              ----------------------------------------------
                              James F. Maroney, III,
                              Vice President, Secretary and General Counsel

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