<PAGE>

                                                                     EXHIBIT 4.4

                                    ANNEX A

                           [FORM OF FACE OF SECURITY]


                      [FORM OF LEGEND FOR GLOBAL SECURITY]

UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE
DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION ("DTC"), TO THE COMPANY OR ITS
AGENT FOR REGISTRATION OF TRANSFERS, EXCHANGE, OR PAYMENT, AND ANY CERTIFICATE
ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME AS IS
REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND ANY PAYMENT IS MADE TO
CEDE & CO. OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED
REPRESENTATIVE OF DTC), ANY TRANSFER, PLEDGE, OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE BY OR TO ANY PERSON IS WRONGFUL INASMUCH AS THE REGISTERED OWNER
HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

TRANSFERS OF THIS GLOBAL SECURITY SHALL BE LIMITED TO TRANSFER IN WHOLE, BUT NOT
IN PART, TO NOMINEES OF DTC OR TO A SUCCESSOR THEREOF OR SUCH SUCCESSOR'S
NOMINEE AND TRANSFERS MADE IN ACCORDANCE WITH THE RESTRICTIONS SET FORTH IN THE
INDENTURE REFERRED TO ON THE REVERSE HEREOF.
<PAGE>

                           COOPER CAMERON CORPORATION

                  1.75% CONVERTIBLE SENIOR DEBENTURE DUE 2021

No.

Issue Date: May 16, 2001                           Stated Maturity: May 17, 2021

Principal Amount:  $200,000,000

                                                              CUSIP:  216640 AB8

     Cooper Cameron Corporation, a Delaware corporation, promises to pay to
______________________ or registered assigns, on May 17, 2021 the Principal
Amount of __________________________________ Dollars ($________________) [or
such greater or lesser Principal Amount as may be shown on Schedule A
hereto].(1)

     This Security will bear interest as specified on the other side of this
Security.  This Security is convertible as specified on the other side of this
Security.

     Additional provisions of this Security are set forth on the other side of
this Security.

     IN WITNESS WHEREOF, Cooper Cameron Corporation has caused this instrument
to be duly executed.

                              COOPER CAMERON CORPORATION


                              By: ______________________________________________
                                  Name:
                                  Title:
                                  Dated:

                    TRUSTEE'S CERTIFICATE OF AUTHENTICATION

     Bank One Trust Company, National Association, as successor to The First
National Bank of Chicago, as Trustee, certifies that this is one of the
Securities referred to in the within-mentioned Indenture.


By  ______________________________________
    Authorized Signatory


________________
(1) For inclusion in the global Security only.

                                       2
<PAGE>

                       [FORM OF REVERSE SIDE OF SECURITY]

                           COOPER CAMERON CORPORATION

                  1.75% CONVERTIBLE SENIOR DEBENTURE DUE 2021

     This Security is one of a duly authorized issue of senior securities of the
Company issued and to be issued in one or more series under an Indenture, dated
as of May 8, 1998, as supplemented by the Supplemental Indenture thereto dated
as of May 16, 2001 relating to the Securities (as so supplemented, herein called
the "Indenture"), between the Company and Bank One Trust Company, National
Association, as successor to The First National Bank of Chicago, as Trustee
(herein called the "Trustee," which term includes any successor trustee under
the Indenture), to which Indenture and all indentures supplemental thereto
reference is hereby made for a statement of the respective rights, limitations
of rights, duties and immunities thereunder of the Company, the Trustee and the
Holders of the Securities and of the terms upon which the Securities are, and
are to be, authenticated and delivered. This Security is one of the series
designated on the face hereof, limited in aggregate principal amount to
$200,000,000.  As used herein, the term "Securities" means securities of the
series designated on the face hereof except that, where the context requires
that such term be construed as including another series of securities (e.g.,
where phases such as "Securities of each series" or "Securities of any series"
or similar phases are used), the term "Securities" means securities of any
series issued or to be issued under the Indenture.

1.  Interest

     This Security will bear interest at the annual rate of 1.75% and will
accrue interest from May 16, 2001 or from the most recent date to which interest
has been paid or provided for.  The Company will pay interest on this Security
twice a year, on May 15 and November 15, beginning on November 15, 2001, to the
person in whose name this Security is registered at the close of business on the
May 1 or November 1 that immediately precedes the date on which interest will be
paid.  Interest will cease to accrue on this Security upon its maturity,
conversion, purchase by the Company at the option of a Holder or redemption.
The Company will calculate interest on the basis of a 360-day year composed of
twelve 30-day months.

2.  Method Of Payment

     Holders must surrender Securities to the Paying Agent to collect all
payments in respect of the Securities.  The Company will pay cash amounts in
money of the United States that at the time of payment is legal tender for
payment of public and private debts.  However, the Company may make such cash
payments by check payable in such money or by wire transfer in immediately
available funds.

3.  Paying Agent, Conversion Agent And Registrar

     Initially, Bank One Trust Company, National Association, as successor to
The First National Bank of Chicago (the "Trustee"), will act as Paying Agent,
Conversion Agent and Registrar.  The Company may appoint and change any Paying
Agent, Conversion Agent, Registrar or co-registrar without notice, other than
notice to the Trustee.  The company or any of

                                       3
<PAGE>

its Subsidiaries or any of their Affiliates may act as Paying Agent, Conversion
Agent, Registrar or co-registrar.

4.  Indenture

     The Company issued the Securities under an Indenture dated as of May 8,
1998, between the Company and the Trustee (as supplemented by the Supplemental
Indenture, the "Indenture") and a Supplemental Indenture dated as of May 16,
2001 between the Company and the Trustee relating to the Securities (the
"Supplemental Indenture").  Capitalized terms used herein and not defined herein
have the meanings ascribed thereto in the Indenture.  The Securities are subject
to all such terms, and Holders are referred to the Indenture for a statement of
those terms.

     The Securities are general unsecured obligations of the Company limited to
$200,000,000 aggregate Principal Amount (subject to Section 102 of the
Supplemental Indenture).  The Indenture does not limit other indebtedness of the
Company, whether secured or unsecured.

5.  Optional Redemption

     There shall be no sinking fund for the retirement of the Securities.  The
Securities are redeemable as a whole, or from time to time in part, at any time
at the option of the Company at the Redemption Prices set forth below, provided
that the Securities are not redeemable prior to May 18, 2006.

     The Redemption Price will be an amount in cash equal to 100% of the
Principal Amount plus accrued and unpaid interest, if any, up to and excluding
the Redemption Date.  The Securities will be redeemable in multiples of $1,000
principal amount.

     If the Company redeems less than all of the outstanding Securities, the
Trustee will select the Securities to be redeemed (i) by lot, (ii) pro rata, or
(iii) by another method the Trustee considers fair and appropriate. If the
Trustee selects a portion of a Holder's Securities for partial redemption and
the Holder converts a portion of the same Securities, the converted portion will
be deemed to be from the portion selected for redemption.

6.   Repurchase at the Option of the Holder; Repurchase at the Option of the
     Holder upon a Fundamental Change

     (a) Subject to the terms and conditions of the Indenture, the Company shall
become obligated to repurchase, at the option of the Holder, the Securities held
by such Holder on May 18, 2006, May 18, 2011 and May 18, 2016 (the "Purchase
Dates") upon delivery of a Purchase Notice as set forth in Section 1108(a)(1) of
the Indenture during the period from the opening of business on the date that is
20 Business Days prior to such Purchase Date until the close of business on such
Purchase Date and upon delivery of the Securities to the Paying Agent by the
Holder.  The "Purchase Price" shall be equal to the Principal Amount plus
accrued and unpaid interest up to and excluding the Purchase Date.  Such
Purchase Prices may be paid, at the option of the Company, in cash or by the
issuance and delivery of shares of Common Stock of the Company, or in any
combination thereof, as set forth in the Indenture.

                                       4
<PAGE>

     Securities in denominations larger than $1,000 of Principal Amount may be
repurchased in part, but only in integral multiples of $1,000 of Principal
Amount.

     (b) At the option of the Holder and subject to the terms and conditions of
the Indenture, the Company shall become obligated to repurchase the Securities
held by such Holder and delivered to the Company or its designated agent on the
date that is 30 days after the date of the Company's notice of a Fundamental
Change occurring on or prior to May 16, 2021 (or if such date is not a Business
Day, the next succeeding Business Day) for a Fundamental Change Purchase Price
equal to the Principal Amount plus accrued and unpaid interest, if any, to the
Fundamental Change Purchase Date which Fundamental Change Purchase Price shall
be paid in cash.  Securities in denominations larger than $1,000 of Principal
Amount may be repurchased in part in connection with a Fundamental Change, but
only in integral multiples of $1,000 of Principal Amount.

     (c) Holders have the right to withdraw any Purchase Notice or Fundamental
Change Purchase Notice, as the case may be, by delivering to the Paying Agent a
written notice of withdrawal in accordance with the provisions of the Indenture.

     (d) If cash (and/or securities if permitted under the Indenture) sufficient
to pay a Purchase Price or Fundamental Change Purchase Price, as the case may
be, of all Securities or portions thereof to be repurchased as of the Purchase
Date or the Fundamental Change Purchase Date, as the case may be, is deposited
with the Paying Agent on the Business Day following the Purchase Date or the
Fundamental Change Purchase Date, as the case may be, interest ceases to accrue
on such Securities (or portions thereof) on and after such date, and the Holder
thereof shall have no other rights as such (other than the right to receive the
Purchase Price or Fundamental Change Purchase Price, as the case may be, upon
surrender of such Security).

7.  Notice of Redemption; Procedures

     Notice of redemption at the option of the Company will be mailed to each
Holder of Securities to be redeemed at the Holder's registered address at least
30 days but not more than 60 days before the Redemption Date.  If money
sufficient to pay the Redemption Price of all Securities (or portions thereof)
to be redeemed on the Redemption Date is deposited with the Paying Agent prior
to or on the Redemption Date, then on and after such date interest ceases to
accrue on such Securities or portions thereof.  Securities in denominations
larger than $1,000 of Principal Amount may be redeemed in part but only in
multiples of $1,000 of Principal Amount.

8.  Ranking

     The Securities rank equally in contractual right of payment with all of the
other existing and future unsubordinated and unsecured indebtedness of the
Company.

9.  Conversion

     Subject to the next two succeeding sentences, a Holder of a Security may
convert this Security for Common Stock of the Company at any time until 5 p.m.,
New York City time on the Stated Maturity.  If this Security is called for
redemption, the Holder may convert it at any time before the close of the third
Business Day prior to the Redemption Date.  A Security in respect of which a
Holder has delivered a notice of exercise of the option to require the Company
to

                                       5
<PAGE>

repurchase such Security or to repurchase such Security in the event of a
Fundamental Change may be converted only if the notice of exercise is withdrawn
in accordance with the terms of the Indenture.

     The initial Conversion Rate is 10.5158 shares of Common Stock per $1,000
Principal Amount, subject to adjustment in certain events described in the
Indenture.  The Company will deliver cash or a check in lieu of any fractional
share of Common Stock.

     Securities surrendered for conversion after the close of business on any
Regular Record Date immediately preceding any Interest Payment Date and prior to
the opening of business of such Interest Payment Date (except Securities or
portions of Securities to be redeemed on a Redemption Date occurring during such
period) must be accompanied by payment from the Holder of an amount equal to the
interest thereon that the registered Holder is to receive from the Company on
such Interest Payment Date. Except where Securities surrendered for conversion
must be accompanied by payment as described above, no interest on converted
Securities will be payable by the Company on any Interest Payment Date
subsequent to the date of conversion.

     To convert this Security a Holder must (1) complete and manually sign the
conversion notice on the back of this Security (or complete and manually sign a
facsimile of such notice) and deliver such notice to the Conversion Agent, (2)
surrender this Security to the Conversion Agent, (3) furnish appropriate
endorsements and transfer documents if required by the Conversion Agent, the
Company or the Trustee and (4) pay any transfer or similar tax, if required.

     A Holder may convert a portion of this Security if the Principal Amount of
such portion is $1,000 or an integral multiple of $1,000.  No payment or
adjustment will be made for dividends on the Common Stock except as provided in
the Indenture.

10.  Conversion Arrangement on Call for Redemption

     Any Securities called for redemption, unless surrendered for conversion
before the close of business on the last Trading Day prior to the Redemption
Date, may be deemed to be purchased from the Holders of such Securities at an
amount not less than the Redemption Price, by one or more investment bankers or
other purchasers who may agree with the Company to purchase such Securities from
the Holders, to convert them for Common Stock and to make payment for such
Securities to the Trustee in trust for such Holders.

11.  Denominations; Transfer; Exchange

     The Securities are in registered form, without coupons, in denominations of
$1,000 of Principal Amount and integral multiples of $1,000.  A Holder may
transfer or convert Securities in accordance with the Indenture.  The Registrar
may require a Holder, among other things, to furnish appropriate endorsements
and transfer documents and to pay any taxes and fees required by law or
permitted by the Indenture.  The Registrar need not transfer or exchange any
Securities selected for redemption (except, in the case of a Security to be
redeemed in part, the portion of the Security not to be redeemed) or any
Securities in respect of which a Purchase Notice or Fundamental Change Purchase
Notice has been given and not withdrawn (except, in the case of a Security to be
purchased in part, the portion of the Security not to be purchased) or any
Securities for a period of 15 days before the mailing of notice of Securities to
be redeemed.

                                       6
<PAGE>

12.  Persons Deemed Owners

     The registered holder of this Security may be treated as the owner of this
Security for all purposes.

13.  Unclaimed Money Or Securities

     The Trustee and the Paying Agent shall return to the Company upon written
request any money or securities held by them for the payment of any amount with
respect to the Securities that remains unclaimed for two years, provided,
however, that the Trustee or such Paying Agent, before being required to make
any such return, shall in the event that the Securities are no longer held in
global form, at the expense of the Company cause to be published once in a
newspaper of general circulation in The City of New York or mail to each such
Holder notice that such money or securities remains unclaimed and that, after a
date specified therein, which shall not be less than 30 days from the date of
such publication or mailing, any unclaimed money or securities then remaining
will be returned to the Company.  After return to the Company, Holders entitled
to the money or securities must look to the Company for payment as general
creditors unless an applicable abandoned property law designates another Person.

14.  Amendment; Waiver

     Subject to certain exceptions set forth in the Indenture, (i) the Indenture
or the Securities may be amended with the written consent of the Holders of at
least a majority in aggregate Principal Amount of the Securities at the time
outstanding (or, in certain cases, of all debt securities under the Indenture)
and (ii) certain Defaults and Events of Defaults may be waived with the written
consent of the Holders of a majority in aggregate Principal Amount of the
Securities at the time outstanding (or, in certain cases, of all debt securities
under the Indenture).  Subject to certain exceptions set forth in the Indenture,
without the consent of any Holder, the Company and the Trustee may amend the
Indenture or the Securities to cure any ambiguity, defect or inconsistency, to
provide for the assumption of the Company's obligations to the Holders of the
Securities in case of a merger or consolidation or sale of all or substantially
all of the Company's assets, to provide for uncertificated Securities in
addition to or in place of certificated Securities, to make any change that does
not adversely affect the rights of any Holder or to comply with any requirement
of the Commission in connection with the qualification of the Indenture under
the Trust Indenture Act.

15.  Limitation on Suits

     Subject to the right of the Holder of any Securities of this series to
institute proceedings to enforce the Holder's right to receive payment of the
principal of and (subject to Section 307 of the Indenture) interest on the
Stated Maturity or Maturities expressed in such Security (or in the case of
redemption, to receive the Redemption Price on the Redemption Date, in the case
of a repurchase, to receive the Purchase Price on the Purchase Date, or in the
case of a Fundamental Change, to receive the Fundamental Change Purchase Price
on the Fundamental Change Purchase Date) and to institute suit for the
enforcement of any such payment on or after such respective dates, and to
receive shares on conversion, no Holder of the Securities of this series shall
have any right to institute any proceeding, judicial or otherwise, with respect
to the

                                       7
<PAGE>

Indenture, or for the appointment of a receiver or trustee, or for any other
remedy hereunder, unless

     (1) an Event of Default with respect to the Securities of this series shall
have occurred and be continuing and such Holder has previously given written
notice to the Trustee of such continuing Event of Default;

     (2) the Holders of not less than 25% in principal amount of the Outstanding
Securities of this series shall have made written request to the Trustee to
institute proceedings in respect of such Event of Default in its own name as
Trustee hereunder;

     (3) such Holder or Holders have offered to the Trustee reasonable indemnity
against the costs, expenses and liabilities to be incurred in compliance with
such request;

     (4) the Trustee for 60 days after its receipt of such notice, request and
offer of indemnity has failed to institute any such proceeding; and

     (5) no direction inconsistent with such written request has been given to
the Trustee during such 60-day period by the Holders of a majority in principal
amount of the Outstanding Securities of this series.

16.  Defaults And Remedies

     If an Event of Default with respect to Securities of this series shall
occur and be continuing, all unpaid Principal Amount plus accrued and unpaid
interest from the date of conversion to the acceleration date of the Securities
of this series may be declared due and payable in the manner and with the effect
provided in the Indenture.

17.  Trustee Dealings With The Company

     The Trustee under the Indenture, in its individual or any other capacity,
may become the owner or pledgee of Securities and may otherwise deal with and
collect obligations owed to it by the Company or its Affiliates and may
otherwise deal with the Company or its Affiliates with the same rights it would
have if it were not Trustee.

18.  No Recourse Against Others

     A director, officer, employee or stockholder, as such, of the Company shall
not have any liability for any obligations of the Company under the Securities
or the Indenture or for any claim based on, in respect of or by reason of such
obligations or their creation.  By accepting a Security, each Holder waives and
releases all such liability.  The waiver and release are part of the
consideration for the issue of the Securities.

19.  Authentication

     This Security shall not be valid until an authorized signatory of the
Trustee manually signs the Trustee's Certificate of Authentication on the other
side of this Security.

                                       8
<PAGE>

20.  Abbreviations

     Customary abbreviations may be used in the name of a Holder or an assignee,
such as TEN COM (=tenants in common), TENANT (=tenants by the entireties), JT
TEN (=joint tenants with right of survivorship and not as tenants in common),
CUST (=custodian), and U/G/M/A (=Uniform Gift to Minors Act).

21.  Governing Law

     THE LAWS OF THE STATE OF NEW YORK SHALL GOVERN THE INDENTURE AND THIS
SECURITY.

22.  Indenture To Control

     In case of any conflict between the provisions of this Security and the
Indenture, the provisions of the Indenture shall control.

     The Company will furnish to any Holder upon written request and without
charge a copy of the Indenture.  Requests may be made to:

               Cooper Cameron Corporation
               515 Post Oak Blvd.
               Suite 1200
               Houston, Texas  77027
               713.513.3300
               Attention:  Corporate Secretary

                                       9
<PAGE>

                               CONVERSION NOTICE

To:  Cooper Cameron Corporation

     The undersigned registered holder of this Security hereby irrevocably
exercises the option to convert this Security, or portion hereof (which is
$1,000 Principal Amount (as defined in the Indenture to which this Security is
subject) or an integral multiple thereof) below designated, for shares of Common
Stock of Cooper Cameron Corporation in accordance with the terms of the
Indenture referred to in this Security, and directs that the shares issuable and
deliverable upon such conversion, together with any check in payment for
fractional shares and any Securities representing any unconverted Principal
Amount hereof, be issued and delivered to the registered holder hereof unless a
different name has been indicated below.  If shares or any portion of this
Security not converted are to be issued in the name of a Person other than the
undersigned, the undersigned will pay all transfer taxes payable with respect
thereto.

Dated:                  ________________________________________________________

                        ________________________________________________________
                                           Signature(s)

Fill in for registration of shares
if to be delivered, and Securities
if to be issued other than to and in
the name of the registered holder:


______________________________________
(Name)


______________________________________
(Street Address)


______________________________________
(City, state and zip code)

Please print name and address

                              Principal Amount to be converted
                              (if less than all):
                              $_________,000
                              Social Security or Other Taxpayer
                              Identification Number:  ____________

                                       10
<PAGE>

             OPTION TO ELECT REPURCHASE UPON A FUNDAMENTAL CHANGE

To:  Cooper Cameron Corporation

     The undersigned registered holder of this Security hereby acknowledges
receipt of a notice from Cooper Cameron Corporation (the "Company") as to the
occurrence of a Fundamental Change with respect to the Company and requests and
instructs the Company to repurchase this Security, or the portion hereof (which
is $1,000 Principal Amount (as defined in the Indenture to which this Security
is subject) or an integral multiple thereof) below designated, in accordance
with the terms of the Indenture referred to in this Security.

Dated: ____________________

                              __________________________________________________
                                                Signature(s)

                              Principal Amount to be repurchased
                              (if less than all):
                              $________,000
                              Social Security or Other Taxpayer
                              Identification Number:  ___________

                                       11
<PAGE>

                                TRANSFER NOTICE

This Transfer Notice relates to $__________ Principal Amount (as defined in the
Indenture to which the referenced Securities are subject) of the 1.75%
Convertible Senior Debentures due 2021 of Cooper Cameron Corporation, a Delaware
corporation, held by ____________ (the "Transferor").

                (I) or (we) assign and transfer this Security to


________________________________________________________________________________
             (Print or type assignee's name, address and zip code)

________________________________________________________________________________


________________________________________________________________________________
              (Insert assignee's social security or tax I.D. no.)

and irrevocably appoint _______________________________ agent to transfer this
Security on the books of the Company.  The agent may substitute another to act
for him.

Your Signature: ________________________________________________________________
          (Sign exactly as your name appears on the other side of this Security)

     Date: _____________________________________________________________________

                                       12
<PAGE>

                                   SCHEDULE A

                 Changes to Principal Amount of Global Security

<TABLE>
<CAPTION>
                           PRINCIPAL AMOUNT OF SECURITIES
                           BY WHICH THIS GLOBAL SECURITY
                           IS TO BE REDUCED OR INCREASED,
                                   AND REASON FOR            REMAINING PRINCIPAL AMOUNT   NOTATION
          DATE                 REDUCTION OR INCREASE          OF THIS GLOBAL SECURITY     MADE BY
______________________     ______________________________    __________________________   ________
<S>                        <C>                               <C>                          <C>

</TABLE>

                                       13