Document:

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                                                                     Exhibit 4.5

                        INCENTIVE STOCK OPTION AGREEMENT
                     (WITH AUTHORIZATION FOR EARLY EXERCISE)

OPTIONEE:
         ---------------------------------------

DATE OF GRANT:
              ----------------------------------

     AGREEMENT between Carbon Energy Corporation (the "Company"), and the above
named Optionee ("Optionee"), an employee of the Company or a Subsidiary thereof.

     The Company and Optionee agree as follows:

1.   GRANT OF OPTION.

     Optionee is hereby granted an Incentive Stock Option, within the meaning of
Section 422 of the Code (the "Option"), to purchase Common Stock of the Company
pursuant to the Carbon Energy Corporation 1999 Stock Option Plan (the "Plan").
The Option and this Agreement are subject to and shall be construed in
accordance with the terms and conditions of the Plan, as now or hereinafter in
effect. Any terms which are used in this Agreement without being defined and
which are defined in the Plan shall have the meaning specified in the Plan.

2.   DATE OF GRANT.

     The date of the grant of the Option is the date first set forth above, the
date of the action by the Plan Administrator in granting the same.

3.   NUMBER AND PRICE OF SHARES.

     The number of shares as to which the Option is granted is the number set
forth in Schedule 3A to this Agreement. The purchase price per share is the
amount set forth in Schedule 3B to this Agreement.

4.   EXPIRATION DATE.

     Unless sooner terminated as provided in Section 5.4 or Section 10 of the
Plan, the Option shall expire and terminate on the date set forth in Schedule 4
to this Agreement, and in no event shall the Option be exercisable after that
date.

5.   MANNER OF EXERCISE.

     Except as provided in this Agreement, the Option shall be exercisable, in
whole or in part, from time to time, in the manner provided in Section 8 of the
Plan.

                                       1
<PAGE>

6.   TIME OF EXERCISE.

     The Option granted hereby shall become vested in and exercisable by
Optionee on the dates and subject to the conditions set forth in Schedule 6 to
this Agreement; provided, however, that Optionee must have been continuously
employed by the Company or a Subsidiary thereof from the date of grant of the
Option until the date specified on Schedule 6 or until the conditions specified
on Schedule 6 have been satisfied.

7.   EARLY EXERCISE.

     Notwithstanding the provisions of Section 6, Optionee may elect at any time
prior to the termination of Optionee's employment with the Company or a
Subsidiary thereof to exercise the Option as to any part or all of the shares
subject to this Option, including without limitation, shares with respect to
which the Option has not yet vested pursuant to Section 6; provided, however,
that (i) a partial exercise of this Option shall be deemed to apply first to
vested shares and then to the earliest vesting installment of unvested shares,
and (ii) upon exercise of the Option with respect to unvested shares, Optionee
shall execute and deliver to the Company an Early Exercise Stock Repurchase
Agreement in substantially the form attached to this Agreement as EXHIBIT A,
which Agreement shall apply with respect to the unvested shares. Execution and
delivery of the Early Exercise Stock Repurchase Agreement prior to the transfer
or delivery of any shares and prior to the expiration of the option period shall
be a condition precedent to the right to purchase such shares. The election
provided in this Section 7 to purchase shares prior to the vesting of the Option
shall cease upon termination of Optionee's employment with the Company or a
Subsidiary thereof and may not be exercised after the date of such termination.

8.   NONTRANSFERABILITY OF OPTION.

     The Option is not transferable by Optionee other than by Will or the laws
of descent and distribution, and the Option shall be exercisable during
Optionee's lifetime only by Optionee; provided that the Optionee may transfer an
Option solely to (i) members of the Optionee's immediate family (children,
grandchildren, or spouse); (ii) trusts for the benefit of such family members;
or (iii) partnerships where the only partners are such family members. Upon any
attempt to transfer, assign, pledge, hypothecate or otherwise dispose of the
Option contrary to the provisions hereof, or upon the levy of any attachment or
similar process upon the Option, the Option shall immediately become null and
void.

9.   WITHHOLDING FOR TAXES.

     Optionee shall reimburse the Company, in cash or by certified or bank
cashier's check, for any federal, state or local taxes required by law to be
withheld with respect to the exercise of the Option or any disqualifying
disposition of the Common Stock acquired upon exercise of the Option. The
Company shall have the right to deduct from any salary or other payments to be
made to Optionee any federal, state or local taxes required by law to be so
withheld. The Company's obligation to deliver a certificate representing the
Common Stock acquired upon exercise of the Option is subject to the payment by
Optionee of any applicable federal, state and local withholding tax.

                                       2
<PAGE>

10.  LEGENDS.

     Certificates representing Common Stock acquired upon exercise of this
Option may contain such legends and transfer restrictions as the Company shall
deem reasonably necessary or desirable, including, without limitation, legends
restricting transfer of the Common Stock until there has been compliance with
federal and state securities laws and until Optionee or any other holder of the
Common Stock has paid the Company such amounts as may be necessary in order to
satisfy any withholding tax liability of the Company resulting from a
disqualifying disposition described in Section 422(a) of the Code.

11.  EMPLOYEE BENEFITS.

     Optionee agrees that the grant and vesting of the Option and the receipt of
shares of Common Stock upon exercise of the Option will constitute special
incentive compensation that will not be taken into account as "salary" or
"compensation" or "bonus" in determining the amount of any payment under any
pension, retirement, profit sharing or other remuneration plan of the Company
unless otherwise provided in such plan.

12.  AMENDMENT.

     Subject to the terms and conditions of the Plan, the Plan Administrator may
modify, extend or renew the Option, or accept the surrender of the Option to the
extent not theretofore exercised and authorize the granting of new Options in
substitution therefor, except that no such action shall diminish or impair the
rights under the Option without the consent of Optionee.

13.  INTERPRETATION.

     The interpretations and constructions of any provision of and
determinations on any question arising under the Plan or this Agreement shall be
made by the Plan Administrator, and all such interpretations, constructions and
determinations shall be final and conclusive as to all parties.

14.  RECEIPT OF PLAN.

     By entering into this Agreement, Optionee acknowledges (i) that he or she
has received and read a copy of the Plan and (ii) that this Agreement is subject
to and shall be construed in accordance with the terms and conditions of the
Plan, as now or hereinafter in effect.

15.  GOVERNING LAW.

     This Agreement shall be construed and shall take effect in accordance with
the laws of the State of Colorado, without regard to the conflicts of laws rules
of such State.

16.  MISCELLANEOUS.

     This Agreement constitutes the entire understanding and agreement of the
parties with respect to the subject matter hereof and supersedes all prior and
contemporaneous agreements or

                                       3
<PAGE>

understandings, inducements or conditions, express or implied, written or oral,
between the parties with respect hereto. If any provision of this Agreement, or
the application thereof, shall for any reason and to any extent be invalid or
unenforceable, the remainder of this Agreement and the application of such
provision to other circumstances shall be interpreted so as best to reasonably
effect the intent of the parties hereto. All notices or other communications
which are required to be given or may be given to either party pursuant to the
terms of this Agreement shall be in writing and shall be delivered personally or
by registered or certified mail, postage prepaid, to the address of the parties
as set forth following the signature of such party. Notice shall be deemed given
on the date of delivery in the case of personal delivery or on the delivery or
refusal date as specified on the return receipt in the case of registered or
certified mail. Either party may change its address for such communications by
giving notice thereof to the other party in conformity with this Section 16.

     IN WITNESS WHEREOF, the Company by a duly authorized officer of the Company
and Optionee have executed this Agreement on _____________, effective as of the
date of grant.

                                        CARBON ENERGY CORPORATION

                                        By:
                                           -------------------------------------
                                        Title:
                                              ----------------------------------
                                        Address: 1700 Broadway, Suite 1150
                                                 Denver, CO 80290
                                                 -------------------------------

                                        OPTIONEE:
                                                 -------------------------------
                                        Address:
                                                --------------------------------

                                       4
<PAGE>

                                    SCHEDULES
                                       TO
                        INCENTIVE STOCK OPTION AGREEMENT
                     (WITH AUTHORIZATION FOR EARLY EXERCISE)

SCHEDULE

3A   Number of Shares of Stock:
                               ------------------

3B   Purchase Price per Share:
                               ------------------

4    Expiration Date:
                               ------------------

6    Vesting Schedule:

<TABLE>
<CAPTION>
                                                   Number of Shares
                 Date                          Which Become Exercisable
                 ----                          ------------------------
<S>                                          <C>

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

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

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

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

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

     ------------------------------          ----------------------------
</TABLE>

     ADDITIONAL CONDITIONS TO VESTING: Notwithstanding the foregoing, no portion
of the Option shall be vested and exercisable until the following conditions
have been satisfied:

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                                       5<PAGE>

                                                                     Exhibit 4.6

                       NONQUALIFIED STOCK OPTION AGREEMENT

OPTIONEE:
         ---------------------------------------

DATE OF GRANT:
              ----------------------------------

     AGREEMENT between Carbon Energy Corporation (the "Company"), and the above
named Optionee ("Optionee").

     The Company and Optionee agree as follows:

1.   GRANT OF OPTION.

     Optionee is hereby granted a Nonqualified Stock Option (the "Option") to
purchase Common Stock of the Company pursuant to the Carbon Energy Corporation
1999 Stock Option Plan (the "Plan"). The Option is not intended to qualify as an
Incentive Stock Option within the meaning of Section 422 of the Code. The Option
and this Agreement are subject to and shall be construed in accordance with the
terms and conditions of the Plan, as now or hereinafter in effect. Any terms
which are used in this Agreement without being defined and which are defined in
the Plan shall have the meaning specified in the Plan.

2.   DATE OF GRANT.

     The date of the grant of the Option is the date first set forth above, the
date of the action by the Plan Administrator in granting the same.

3.   NUMBER AND PRICE OF SHARES.

     The number of shares as to which the Option is granted is the number set
forth in Schedule 3A to this Agreement. The purchase price per share is the
amount set forth in Schedule 3B to this Agreement.

4.   EXPIRATION DATE.

     Unless sooner terminated as provided in Section 5.4 or Section 10 of the
Plan, the Option shall expire and terminate on the date set forth in Schedule 4
to this Agreement, and in no event shall the Option be exercisable after that
date.

5.   MANNER OF EXERCISE.

     Except as provided in this Agreement, the Option shall be exercisable, in
whole or in part, from time to time, in the manner provided in Section 8 of the
Plan.

                                       1
<PAGE>

6.   TIME OF EXERCISE.

     The Option granted hereby shall become vested in and exercisable by
Optionee on the dates and subject to the conditions set forth in Schedule 6 to
this Agreement; provided, however, that Optionee must have been continuously
employed by the Company or a Subsidiary thereof from the date of grant of the
Option until the date specified on Schedule 6 or until the conditions specified
on Schedule 6 have been satisfied.

7.   NONTRANSFERABILITY OF OPTION.

     The Option is not transferable by Optionee other than by Will or the laws
of descent and distribution, and the Option shall be exercisable during
Optionee's lifetime only by Optionee; provided that the Optionee may transfer an
Option solely to (i) members of the Optionee's immediate family (children,
grandchildren, or spouse); (ii) trusts for the benefit of such family members;
or (iii) partnerships where the only partners are such family members. Upon any
attempt to transfer, assign, pledge, hypothecate or otherwise dispose of the
Option contrary to the provisions hereof, or upon the levy of any attachment or
similar process upon the Option, the Option shall immediately become null and
void.

8.   WITHHOLDING FOR TAXES.

     Optionee shall reimburse the Company, in cash or by certified or bank
cashier's check, for any federal, state or local taxes required by law to be
withheld with respect to the exercise of the Option. The Company shall have the
right to deduct from any salary or other payments to be made to Optionee any
federal, state or local taxes required by law to be so withheld. The Company's
obligation to deliver a certificate representing the Common Stock acquired upon
exercise of the Option is subject to the payment by Optionee of any applicable
federal, state and local withholding tax.

9.   LEGENDS.

     Certificates representing Common Stock acquired upon exercise of this
Option may contain such legends and transfer restrictions as the Company shall
deem reasonably necessary or desirable, including, without limitation, legends
restricting transfer of the Common Stock until there has been compliance with
federal and state securities laws.

10.  EMPLOYEE BENEFITS.

     Optionee agrees that the grant and vesting of the Option and the receipt of
shares of Common Stock upon exercise of the Option will constitute special
incentive compensation that will not be taken into account as "salary" or
"compensation" or "bonus" in determining the amount of any payment under any
pension, retirement, profit sharing or other remuneration plan of the Company
unless otherwise provided in such plan.

11.  AMENDMENT.

     Subject to the terms and conditions of the Plan, the Plan Administrator may
modify, extend or renew the Option, or accept the surrender of the Option to the
extent not theretofore

                                       2
<PAGE>

exercised and authorize the granting of new Options in substitution therefor,
except that no such action shall diminish or impair the rights under the Option
without the consent of Optionee.

12.  INTERPRETATION.

     The interpretations and constructions of any provision of and
determinations on any question arising under the Plan or this Agreement shall be
made by the Plan Administrator, and all such interpretations, constructions and
determinations shall be final and conclusive as to all parties.

13.  RECEIPT OF PLAN.

     By entering into this Agreement, Optionee acknowledges (i) that he or she
has received and read a copy of the Plan and (ii) that this Agreement is subject
to and shall be construed in accordance with the terms and conditions of the
Plan, as now or hereinafter in effect.

14.  GOVERNING LAW.

     This Agreement shall be construed and shall take effect in accordance with
the laws of the State of Colorado, without regard to the conflicts of laws rules
of such State.

15.  MISCELLANEOUS.

     This Agreement constitutes the entire understanding and agreement of the
parties with respect to the subject matter hereof and supersedes all prior and
contemporaneous agreements or understandings, inducements or conditions, express
or implied, written or oral, between the parties with respect hereto. If any
provision of this Agreement, or the application thereof, shall for any reason
and to any extent be invalid or unenforceable, the remainder of this Agreement
and the application of such provision to other circumstances shall be
interpreted so as best to reasonably effect the intent of the parties hereto.
All notices or other communications which are required to be given or may be
given to either party pursuant to the terms of this Agreement shall be in
writing and shall be delivered personally or by registered or certified mail,
postage prepaid, to the address of the parties as set forth following the
signature of such party. Notice shall be deemed given on the date of delivery in
the case of personal delivery or on the delivery or refusal date as specified on
the return receipt in the case of registered or certified mail. Either party may
change its address for such communications by giving notice thereof to the other
party in conformity with this Section 15.

                                       3
<PAGE>

     IN WITNESS WHEREOF, the Company by a duly authorized officer of the Company
and Optionee have executed this Agreement on _____________, effective as of the
date of grant.

                                        CARBON ENERGY CORPORATION

                                        By:
                                           -------------------------------------
                                        Title:
                                              ----------------------------------
                                        Address: 1700 Broadway, Suite 1150
                                                 Denver, CO 80290
                                                 -------------------------------

                                        OPTIONEE:
                                                 -------------------------------
                                        Address:
                                                --------------------------------

                                       4
<PAGE>

                                   SCHEDULES
                                       TO
                       NONQUALIFIED STOCK OPTION AGREEMENT

SCHEDULE

3A   Number of Shares of Stock:
                               ------------------

3B   Purchase Price per Share:
                               ------------------

4    Expiration Date:
                               ------------------

6    Vesting Schedule:

<TABLE>
<CAPTION>
                                                   Number of Shares
                 Date                          Which Become Exercisable
                 ----                          ------------------------
<S>                                          <C>

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

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

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

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

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

     ------------------------------          ----------------------------
</TABLE>

     ADDITIONAL CONDITIONS TO VESTING: Notwithstanding the foregoing, no portion
of the Option shall be vested and exercisable until the following conditions
have been satisfied:

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