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                                                                    EXHIBIT 10.4









                              EMPLOYMENT AGREEMENT
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                               TABLE OF CONTENTS
<TABLE>
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                                                                                        Page
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<S>  <C>                                                                                <C>
 
1.   Employment Period................................................................    1
2.   Terms of Employment..............................................................    1
     (a)  Position and Duties.........................................................    1
     (b)  Compensation................................................................    2
          (i) Base Salary.............................................................    2
          (ii) Annual Bonus...........................................................    2
          (iii) Incentive, Savings and Retirement Plans...............................    3
          (iv) Welfare Benefit Plans..................................................    3
          (v) Expenses................................................................    3
          (vi) Fringe Benefits and Perquisites........................................    3
          (vii) Office and Support Staff..............................................    3
          (viii) Vacation.............................................................    4
          (ix) Stock Option Grants....................................................    4
          (x) Restricted Stock and Other Equity-Based Grants..........................    4
          (xi) Life Insurance.........................................................    4
3.   Termination of Employment........................................................    5
     (a)  Death or Disability.........................................................    5
     (b)  Cause.......................................................................    5
     (c)  Good Reason; Window Period..................................................    6
     (d)  Notice of Termination.......................................................    7
     (e)  Date of Termination.........................................................    7
4.   Obligations of the Company upon Termination......................................    7
     (a)  Disability, Good Reason or During a Window Period; Other than for Cause.....    7
     (b)  Death (except during a Window Period).......................................   10
     (c)  Cause; Other than for Disability, Good Reason or During a Window Period.....   10
5.   Non-exclusivity of Rights........................................................   11
6.   Full Settlement; Resolution of Disputes..........................................   11
7.   Certain Additional Payments by the Company.......................................   12
8.   Confidential Information.........................................................   15
9.   Change of Control................................................................   15
10.  Covenant Not to Compete..........................................................   19
11.  Successors.......................................................................   20
12.  Miscellaneous....................................................................   21
</TABLE>

                                      -i-
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                              EMPLOYMENT AGREEMENT


          This AGREEMENT (the "Agreement")  by and between Edge Petroleum
Corporation, a Delaware corporation (the "Company"), and John E. Calaway (the
"Executive"), dated as of the 25th day of February, 1997 and to be effective as
of the Agreement Effective Date (as defined in Section 12(h) hereof).

          In entering into this Agreement, the Board of Directors of the Company
(the "Board") desires to provide the Executive with substantial incentives to
serve the Company as one of its senior executives performing at the highest
level of leadership and stewardship, without distraction or concern over minimum
compensation, benefits or tenure, to manage the Company's future growth and
development, and maximize the returns to the Company's stockholders.

                NOW, THEREFORE, IT IS HEREBY AGREED AS FOLLOWS:

          1. Employment Period. As of the Agreement Effective Date (hereinafter
defined), the Company hereby agrees to employ the Executive and the Executive
hereby agrees to accept employment with the Company, in accordance with, and
subject to, the terms and provisions of this Agreement, for the period (the
"Employment Period") commencing on the Agreement Effective Date and ending on
the fifth anniversary of the Agreement Effective Date; provided, on the second
anniversary of the Agreement Effective Date and each anniversary of the
Agreement Effective Date thereafter, the Employment Period shall automatically
renew for an additional one year without any further action by either the
Company or the Executive, it being the intention of the parties that there shall
be continuously a remaining term of not less than three years' duration of the
Employment Period until an event has occurred as described in, or one of the
parties shall have made an appropriate election pursuant to, the provisions of
Section 3.


          2. Terms of Employment.

     (a)  Position and Duties.

     (i) During the Employment Period, (A) the Executive's position (including
status, offices, titles and reporting requirements), authority, duties and
responsibilities shall be at least commensurate in all material respects with
the most significant of those held, exercised and assigned on the Agreement
Effective Date, which shall in any event include status as Chairman of the Board
and Chief Executive Officer of the Company, and (B) the Executive's services
shall be performed within the Houston, Texas metropolitan area.

     (ii) During the Employment Period, and excluding any periods of vacation
and sick leave to which the Executive is entitled, the Executive agrees to
devote full attention and time during normal business hours to the business and
affairs of the Company and, to the extent necessary to discharge the
responsibilities assigned to the Executive hereunder, to use

                                       1
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the Executive's reasonable best efforts to perform faithfully and efficiently
such responsibilities.  During the Employment Period, it shall not be a
violation of this Agreement for the Executive to (A) serve on corporate, civic
or charitable boards or committees, (B) deliver lectures, fulfill speaking
engagements or teach at educational institutions and (C) manage personal
investments, so long as such activities do not interfere with the performance of
the Executive's responsibilities as an employee of the Company in accordance
with this Agreement.  It is expressly understood and agreed that to the extent
that any such activities have been conducted by the Executive prior to the
Agreement Effective Date, the continued conduct of such activities (or the
conduct of activities similar in nature and scope thereto) subsequent to the
Agreement Effective Date shall not thereafter be deemed to interfere with the
performance of the Executive's responsibilities to the Company.

     (b)  Compensation.
          ------------ 

     (i) Base Salary.  During the Employment Period, the Executive shall receive
an annual base salary equal to the base salary in effect immediately prior to
the Agreement Effective Date ("Annual Base Salary"), which shall be paid on a
semimonthly basis.  During the Employment Period, the Annual Base Salary shall
be reviewed at least annually and shall be increased at any time and from time
to time as shall be substantially consistent with increases in base salary
generally awarded in the ordinary course of business to executives of the
Company and its affiliated companies.  Any increase in Annual Base Salary shall
not serve to limit or reduce any other obligation to the Executive under this
Agreement.  Annual Base Salary shall not be reduced after any such increase and
the term "Annual Base Salary," as utilized in this Agreement, shall refer to
Annual Base Salary as so increased.  As used in this Agreement, the term
"affiliated companies" shall include, when used with reference to the Company,
any company controlled by, controlling or under common control with the Company.

     (ii) Annual Bonus.  In addition to Annual Base Salary, the Executive shall
be awarded, for each fiscal year or portion thereof during the Employment
Period, an Annual Bonus (the "Annual Bonus"), in cash equal to the amount
determined in the following table based on the Company's audited annual net cash
flow increase relative to the audited net cash flow of the Company for the prior
calendar year:

<TABLE>
<CAPTION>

  Percent of Increase
In Audited Net Cash Flow             Bonus Amount
------------------------             ------------
 
<S>                                   <C>
Less than 15%.......................        0
Greater than 15% and less than 25%..   50,000
Greater than 25%....................  105,000
</TABLE>

     (iii)  Incentive, Savings and Retirement Plans.  During the Employment
Period, the Executive shall be entitled to participate in all incentive, savings
and retirement plans that

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are tax-qualified under Section 401(a) of the Internal Revenue Code of 1986, as
amended ("Code"), and all plans that are supplemental to any such tax-qualified
plans, in each case to the extent that such plans are applicable generally to
other executives of the Company and its affiliated companies, but in no event
shall such plans provide the Executive with incentive opportunities (measured
with respect to both regular and special incentive opportunities, to the extent,
if any, that such distinction is applicable), savings opportunities and
retirement benefit opportunities that are, in each case, less favorable to the
Executive, in the aggregate, than the most favorable plans  of the Company and
its affiliated companies.  As used in this Agreement, the term "most favorable"
shall, when used with reference to any plans, practices, policies or programs of
the Company and its affiliated companies, be deemed to refer to the plans,
practices, policies or programs of the Company and its affiliated companies, as
in effect at any time during the Employment Period and provided generally to
other executives of the Company or its affiliated companies, which are most
favorable to the Executive.

     (iv) Welfare Benefit Plans.  During the Employment Period, the Executive
and/or the Executive's family, as the case may be, shall be eligible for
participation in and shall receive all benefits under welfare benefit plans,
practices, policies and programs provided by the Company or its affiliated
companies  (including, without limitation, medical, prescription, dental,
vision, disability, salary continuance, group life and supplemental group life,
accidental death and travel accident insurance plans and programs) to the extent
applicable generally to other executives of the Company or its affiliated
companies, but in no event shall such plans, practices, policies and programs
provide the Executive with benefits that are less favorable, in the aggregate,
than the most favorable such plans, practices, policies and programs of the
Company and its affiliated companies.

     (v) Expenses.  During the Employment Period, the Executive shall be
entitled to receive prompt reimbursement for all reasonable expenses incurred by
the Executive in accordance with the most favorable policies, practices and
procedures of the Company and its affiliated companies.

     (vi) Fringe Benefits and Perquisites.  During the Employment Period, the
Executive shall be entitled to fringe benefits and perquisites in accordance
with the most favorable plans, practices, programs and policies of the Company
and its affiliated companies applicable to similarly situated executives.

     (vii)  Office and Support Staff.  During the Employment Period, the
Executive shall be entitled to an office or offices of a size and with
furnishings and other appointments, and to secretarial and other assistance to
the extent needed to fulfill his corporate responsibilities, at least equal to
the most favorable of the foregoing provided to the Executive by the Company and
its affiliated companies at any time during the Employment Period.

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     (viii)  Vacation.  During the Employment Period, the Executive shall be
entitled to paid vacation in accordance with the most favorable plans, policies,
programs and practices of the Company and its affiliated companies.

     (ix) Stock Option Grants.  Prior to or contemporaneously with the execution
of this Agreement, Executive has been granted stock options on 133,645 shares of
Company common stock, par value $.01 per share ("Common Stock"), at an exercise
price equal to the IPO Price ("Initial Stock Option").  The Initial Stock Option
has a term of 10 years and is exercisable in cumulative annual increments of
one-fifth of the total number of shares subject to the option, beginning on the
first anniversary of the Date of Grant.  "IPO" shall mean the initial public
offering of Common Stock pursuant to which the Company receives payment in cash
for shares of its Common Stock that it sells pursuant to a registration
statement on Form S-1 filed and declared effective under the Securities Act of
1933.  "IPO Price" shall mean the per share price to the public for the Common
Stock sold in the IPO, as set forth on the cover page of the final prospectus
for the IPO.

     (x) Restricted Stock and Other Equity-Based Grants.  Prior to or
contemporaneously with the execution of this Agreement, Executive has been
granted a restricted stock award of 66,823 shares of Company Common Stock that
will vest ratably over five years, beginning with the first anniversary of the
date of grant, and an additional 66,823 shares of Company Common Stock that will
vest on the earlier to occur of 10 years from the date of grant or the
achievement of certain performance goals ("Initial Restricted Stock Grant").
The tranche of Initial Restricted Stock Grant subject to performance goals will
vest earlier than 10 years only if the average closing price per share of Common
Stock for the month of December of any year, as compared with the month of
January for the same year (the "Annual Growth"), has increased by 25% or more,
then only 20% of the tranche will vest.  If the Annual Growth for a particular
year is not at least 25% and as a result none of the tranche vests for such a
year (a "Nonachieving Year"), then a deficit equal to 25% less the Nonachieving
Year Annual Growth shall exist.  In the year subsequent to a Nonachieving Year,
an additional 20% of the performance share tranche will vest if the Annual
Growth for such subsequent year is at least 25% plus the deficit for the
Nonachieving Year.

     (xi) Life Insurance.  Within 60 days of the Agreement Effective Date,
Executive shall be provided term life insurance coverage in an amount not less
than $2,000,000 during the succeeding portion of the Employment Period; provided
that such coverage can be purchased at standard rates within such 60 days of the
Agreement Effective Date.

     3.  Termination of Employment.
         -------------------------- 

          (a) Death or Disability.  The Executive's employment shall terminate
automatically upon the Executive's death during the Employment Period.  If the
Company determines in good faith that the Disability of the Executive has
occurred during the Employment Period (pursuant to the definition of Disability
set forth below), it may give to the Executive written 

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notice in accordance with Section 11(d) of this Agreement of its intention to
terminate the Executive's employment. In such event, the Executive's employment
with the Company shall terminate effective on the 30th day after receipt of such
notice by the Executive (the "Disability Effective Date"), provided that, within
the 30 days after such receipt, the Executive shall not have returned to full-
time performance of the Executive's duties. For purposes of this Agreement,
"Disability" shall mean the absence of the Executive from the Executive's duties
with the Company on a full-time basis for either (i) 180 consecutive business
days or (ii) in any two-year period 270 nonconsecutive business days as a result
of incapacity due to mental or physical illness which is determined to be total
and permanent by a physician selected by the Company or its insurers and
acceptable to the Executive or the Executive's legal representative (such
agreement as to acceptability not to be withheld unreasonably).

          (b) Cause.  The Company may terminate the Executive's employment
during the Employment Period for Cause.  For purposes of this Agreement, "Cause"
shall mean for the Company's termination of the Executive's employment:  (i) the
Executive's final conviction of a felony crime that enriched the Executive at
the expense of the Company; provided, however, that after indictment, the
Company may suspend Executive from the rendition of services, but without
limiting or modifying in any other way the Company's obligations under this
Agreement; (ii) a material breach by Executive of a material fiduciary duty owed
to the Company; (iii) a material breach by Executive of any of the covenants
made by him in Sections 8 and 10 hereof; (iv) the willful and gross neglect by
Executive of the material duties specifically and expressly required by this
Agreement; or (v) the Executive's continuing failure to substantially perform
his duties and responsibilities hereunder (except by reason of the Executive's
incapacity due to physical or mental illness or injury) for a period of 45 days
after the Required Board Majority, as defined herein, has delivered to the
Executive a written demand for substantial performance hereunder which
specifically identifies the bases for the Required Board Majority's
determination that the Executive has not substantially performed his duties and
responsibilities hereunder (that period being the "Grace Period"); provided,
that for purposes of this clause (v), the Company shall not have Cause to
terminate the Executive's employment unless (A) at a meeting of the Board called
and held following the Grace Period in the city in which the Company's principal
executive offices are located, of which the Executive was given not less than 10
days' prior written notice and at which the Executive was afforded the
opportunity to be represented by counsel, appear and be heard, the Required
Board Majority shall adopt a written resolution which (1) sets forth the
Required Board Majority's determination that the failure of the Executive to
substantially perform his duties and responsibilities hereunder has (except by
reason of his incapacity due to physical or mental illness or injury) continued
past the Grace Period and (2) specifically identifies the bases for that
determination, and (B) the Company, at the written direction of the Required
Board Majority, shall deliver to the Executive a Notice of Termination for Cause
to which a copy of that resolution, certified as being true and correct by the
secretary or any assistant secretary of the Company, is attached.  "Required
Board Majority" means at any time a majority of the members of the Board at that
time which includes at least a majority of the Directors, each of whom has not
been an employee of the Company or any subsidiary of the Company.

                                       5
<PAGE>
 
          (c) Good Reason; Window Period.  The Executive's employment may be
terminated during the Employment Period by the Executive for Good Reason, or
during a Window Period by the Executive without any reason.  For purposes of
this Agreement, "Window Period" shall mean the 60-day period immediately
following elapse of one year after any Change of Control as defined in Section 9
of this Agreement.  For purposes of this Agreement, "Good Reason" shall mean:

          (i) the assignment to the Executive of any duties materially
inconsistent in any respect with the Executive's position (including status,
offices, titles and reporting requirements), authority, duties or
responsibilities as contemplated by Section 2 of this Agreement, or any other
action by the Company which results in a diminution in such position, authority,
duties or responsibilities, excluding for this purpose an isolated,
insubstantial and inadvertent action not taken in bad faith and which is
remedied by the Company promptly after receipt of notice thereof given by the
Executive;

          (ii) any material failure by the Company to comply with any of the
provisions of this Agreement, other than an isolated, insubstantial and
inadvertent failure not occurring in bad faith and which is remedied by the
Company promptly after receipt of notice thereof given by the Executive;

          (iii) the Company's requiring the Executive to be based at any office
outside the Houston metropolitan area;

          (iv) any purported termination by the Company of the Executive's
employment otherwise than as expressly permitted by this Agreement;

          (v) any failure by the Company to comply with and satisfy the
requirements of Section 11 of this Agreement, provided that (A) the successor
described in Section 11(c) has received, at least 10 days prior to the Date of
Termination (as defined in subparagraph (e) below), written notice from the
Company or the Executive of the requirements of such provision and (B) such
failure to be in compliance and satisfy the requirements of Section 11 shall
continue as of the Date of Termination; or

          (vi) any failure to reelect Executive as a member of the Board and
Chairman of the Board.

          (d) Notice of Termination.  Any termination by the Company for Cause,
or by the Executive for Good Reason or without any reason during a Window
Period, shall be communicated by Notice of Termination to the other party hereto
given in accordance with Section 12(d) of this Agreement.  The failure by the
Executive or the Company to set forth in the Notice of Termination any fact or
circumstance which contributes to a showing of Good Reason or Cause shall not
waive any right of the Executive or the Company hereunder or preclude the

                                       6
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Executive or the Company from asserting such fact or circumstance in enforcing
the Executive's or the Company's rights hereunder.

          (e) Date of Termination.  For purposes of this Agreement, the term
"Date of Termination" means (i) if the Executive's employment is terminated by
the Company for Cause, or by the Executive during a Window Period or for Good
Reason, the date of receipt of the Notice of Termination or any later date
specified therein, as the case may be, (ii) if the Executive's employment is
terminated by the Company other than for Cause or Disability, the Date of
Termination shall be the date on which the Company notifies the Executive of
such termination and (iii) if the Executive's employment is terminated by reason
of death or Disability, the Date of Termination shall be the date of death of
the Executive or the Disability Effective Date, as the case may be.

          4.  Obligations of the Company upon Termination.
              --------------------------------------------

          (a) Disability, Good Reason or During a Window Period; Other than for
Cause or Death (except during a Window Period).  If, during the Employment
Period, the Company shall terminate the Executive's employment other than for
Cause, including a termination by reason of Disability (but not by reason of
death), or the Executive shall terminate employment for Good Reason or his
employment shall be terminated during a Window Period by the Company for Cause,
by the Executive without any reason, or by reason of death:

     (i) the Company shall pay or provide to or in respect of the Executive the
following amounts and benefits:

     A.  in a lump sum in cash, within 10 days after the Date of Termination, an
amount equal to the sum of (1) the Executive's Annual Base Salary through the
Date of Termination, (2) any deferred compensation previously awarded to or
earned by the Executive (together with any accrued interest or earnings thereon)
and (3) any compensation for unused vacation time for which the Executive is
eligible in accordance with the most favorable plans, policies, programs and
practices of the Company and its affiliated companies, in each case to the
extent not theretofore paid (the sum of the amounts described in clauses (1),
(2) and (3) shall be hereinafter referred to as the "Accrued Obligation");

     B.  in a lump sum in cash, discounted at 6%, within 10 days after the Date
of Termination, an amount equal to 125% of Annual Base Salary that would have
been paid to the Executive pursuant to this Agreement for the period (the
"Remaining Employment Period") beginning on the Date of Termination and ending
on the latest possible date of termination of the Employment Period in
accordance with the provisions of Section 1 hereof (the "Final Expiration Date")
if the Executive's employment had not been terminated;

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     C.  continuation for the Remaining Employment Period of life insurance and
medical benefits coverages, but with the Company's medical benefits coverages
being secondary to any coverages provided by another employer;

     D.  effective as of the Date of Termination, (1) immediate vesting and
exercisability of, and termination of any restrictions on sale or transfer
(other than any such restriction arising by operation of law) with respect to,
each and every stock option, restricted stock award, restricted stock unit award
and other equity-based award and performance award (each, a "Compensatory
Award") that is outstanding as of a time immediately prior to the Date of
Termination except that the portion of any restricted stock award described in
Section 2(b)(x) that would vest only by reason of a achievement of performance
goals and not solely by reason of continued employment shall vest only if
termination is by the Company without Cause or by Employee for Good Reason or in
a Window Period and either (w) termination occurs in the first year of the
Employment Period in which event the unvested portion shall be 100% vested, (x)
termination occurs in the second year of the Employment Period in which event
80% of the unvested portion shall be vested, (y) termination occurs in the third
year of the Employment Period in which event 60% of the unvested portion shall
be vested or (z) termination occurs after the third year of the Employment
Period and the performance goals have been met in each of the first three years
of the Employment Period in which event all unvested shares shall be vested, (2)
the extension of the term during which each and every Compensatory Award may be
exercised by the Executive until the earlier of (x) the first anniversary of the
Date of Termination or (y) the date upon which the right to exercise any
Compensatory Award would have expired if the Executive had continued to be
employed by the Company under the terms of this Agreement until the Final
Expiration Date and (3) at the sole election of Executive, in exchange for any
or all Compensatory Awards that are either denominated in or payable in Common
Stock, an amount in cash equal to the excess of (x) the Highest Price Per Share
(as defined below) over (y) the exercise or purchase price, if any, of such
Compensatory Awards.  As used herein, the term "Highest Price Per Share" shall
mean the highest price per share that can be determined to have been paid or
agreed to be paid for any share of Common Stock by a Covered Person (as defined
below) at any time during the Employment Period or the six-month period
immediately preceding the Agreement Effective Date.  As used herein, the term
"Covered Person" shall mean any Person other than an Exempt Person (in each case
as defined in Section 9 hereof) who (I) is the Beneficial Owner (as defined in
Section 9 hereof) of 10% or more of the outstanding shares of Common Stock or
10% or more of the combined voting power of the outstanding Voting Stock (as
defined in Section 9 hereof) of the Company at any time during the Employment
Period, (II) is a Person who has any material involvement in proposing or
effectuating the Change of Control (as defined in Section 9 hereof) or (III) is
an assignee of or has otherwise succeeded to any shares of Common Stock or
Voting Stock of the Company which were at any time during

                                       8
<PAGE>
 
the Employment Period "beneficially owned" (as defined in Section 9 hereof) by
any Person identified in clause (I) or (II) of this definition, if such
assignment or succession shall have occurred in the course of a privately
negotiated transaction rather than an open market transaction.  For purposes of
determining whether a Person is a Covered Person, the number of shares of Common
Stock or Voting Stock of the Company deemed to be outstanding shall include
shares of which the Person is deemed the Beneficial Owner, but shall not include
any other shares which may be issuable pursuant to any agreement, arrangement or
understanding, or upon exercise of conversion rights, warrants or options.  In
determining the Highest Price Per Share, the price paid or agreed to be paid by
a Covered Person will be appropriately adjusted to take into account (W)
distributions paid or payable in stock, (X) subdivisions of outstanding stock,
(Y) combinations of shares of stock into a smaller number of shares and (Z)
similar events; and

     E.  as soon as practicable following the calendar year of the date of
termination, an amount equal to the product of (x) the Annual Bonus that would
have been paid to Executive with respect to the year of termination had the Date
of Termination not occurred and (y) a fraction, the numerator of which is the
number of days in the fiscal year through the Date of Termination and the
denominator of which is 365;

     (ii) for the Remaining Employment Period, or such longer period as any
plan, program, practice or policy may provide, the Company shall continue
benefits to the Executive and/or the Executive's family at least equal to those
which would have been provided to them in accordance with the plans, programs,
practices and policies described in Sections 2(b)(iv) of this Agreement if the
Executive's employment had not been terminated in accordance with the most
favorable plans, practices, programs or policies of the Company and its
affiliated companies (such continuation of such benefits for the applicable
period herein set forth shall be hereinafter referred to as "Welfare Benefit
Continuation").  For purposes of determining eligibility of the Executive for
retiree benefits pursuant to such plans, practices, programs and policies, the
Executive shall be considered to have remained employed until the Final
Expiration Date and to have retired on such date.

          (b) Death (except during a Window Period).  If the Executive's
employment is terminated by reason of the Executive's death during the
Employment Period and other than during a Window Period in which event the
provisions of Section 4(a) shall govern, this Agreement shall terminate without
further obligations to the Executive's legal representatives under this
Agreement, other than (i) the payment of Accrued Obligations (which shall be
paid to the Executive's estate or beneficiary, as applicable, in a lump sum in
cash within 30 days of the Date of Termination), (ii) the payment of an amount
equal to the Annual Salary that would have been paid to the Executive pursuant
to this Agreement for the period beginning on the Date of Termination and ending
on the first anniversary thereof if the Executive's employment had not
terminated by reason of death (which shall be paid to the Executive's estate or
beneficiary, as applicable, in a lump sum in cash within 30

                                       9
<PAGE>
 
days of the Date of Termination), (iii) during the period beginning on the Date
of Termination and ending on the first anniversary thereof medical benefits
coverage determined as if Executive's employment had not terminated by reason of
death, (iv) as soon as practicable following the fiscal year in which death
occurs, payment of an amount equal to the product of (x) the Annual Bonus that
would have been paid to Executive with respect to the year of termination had
the Date of Termination not occurred and (y) a fraction, the numerator of which
is the number of days in the fiscal year through the Date of Termination and the
denominator of which is 365 and (v) effective as of the Date of Termination, (A)
immediate vesting and exercisability of, and termination of any restrictions on
sale or transfer  (other than any such restriction arising by operation of law)
with respect to, each and every Compensatory Award  outstanding as of a time
immediately prior to the Date of Termination except the portion of any
restricted stock award described in Section 2(b)(x) that would vest only by
reason of achievement of performance goals and not by solely by reason of
continued employment shall vest only if either (w) death occurs in the first
year of the Employment Period in which event the unvested portion shall be 100%
vested, (x) death occurs in the second year of the Employment Period in which
event 80% of the unvested portion shall be vested, (y) death occurs in the third
year of the Employment Period in which event 60% of the unvested portion shall
be vested or (z) death occurs after the third year of the Employment Period and
the performance goals have been met in each of the first three years of the
Employment Period in which event all unvested shares shall be vested, (B) the
extension of the term during which each and every Compensatory Award may be
exercised or purchased by the Executive until the earlier of (1) the first
anniversary of the Date of Termination or (2) the date upon which the right to
exercise or purchase any Compensatory Award would have expired if the Executive
had continued to be employed by the Company under the terms of this Agreement
until the Final Expiration Date and (C) at the sole election of the Executive's
legal representative, in exchange for any Compensatory Award that is either
denominated in or payable in Common Stock, an amount in cash equal to the excess
of (1) the Highest Price Per Share over (2) the exercise or purchase price, if
any, of such Compensatory Award.

          (c) Cause; Other than for Disability, Good Reason or During a Window
Period.  If the Executive's employment shall be terminated for Cause during the
Employment Period and other than during a Window Period, in which event the
provisions of Section 4(a) shall govern, this Agreement shall terminate without
further obligations to the Executive other than for Accrued Obligations.  If the
Executive terminates employment during the Employment Period, excluding a
termination for any of Disability, Good Reason or without any reason during a
Window Period, in which event the provisions of Section 4(a) shall govern, this
Agreement shall terminate without further obligations to the Executive, other
than for the payment of Accrued Obligations.  In such case, all Accrued
Obligations shall be paid to the Executive in a lump sum in cash within 30 days
of the Date of Termination.

          5.  Non-exclusivity of Rights.  Except as provided in Section 4 of
this Agreement, nothing in this Agreement shall prevent or limit the Executive's
continuing or future participation in any plan, program, policy or practice
provided by the Company or any of its affiliated companies and for which the
Executive may qualify, nor shall anything herein limit or 

                                       10
<PAGE>
 
otherwise affect such rights as the Executive may have under any contract or
agreement with the Company or any of its affiliated companies. Amounts which are
vested benefits or which the Executive is otherwise entitled to receive under
any plan, policy, practice or program of or any contract or agreement with the
Company or any of its affiliated companies at or subsequent to the Date of
Termination shall be payable in accordance with such plan, policy, practice or
program or contract or agreement except as such plan, policy, practice or
program is superseded by this Agreement.

          6.  Full Settlement; Resolution of Disputes.
              ---------------------------------------- 

          (a) The Company's obligation to make payments provided for in this
Agreement and otherwise to perform its obligations hereunder shall not be
affected by any setoff, counterclaim, recoupment, defense, mitigation or other
claim, right or action which the Company may have against the Executive or
others.  The Company agrees to pay promptly as incurred, to the full extent
permitted by law, all legal fees and expenses which the Executive may reasonably
incur as a result of any contest (regardless of the outcome thereof) by the
Company, the Executive or others of the validity or enforceability of, or
liability under, any provision of this Agreement or any guarantee of performance
thereof (including as a result of any contest by the Executive about the amount
of any such payment pursuant to this Agreement), plus in each case interest on
any delayed payment at the annual percentage rate which is three percentage
points above the interest rate shown as the Prime Rate in the Money Rates column
in the then most recently published edition of The Wall Street Journal
(Southwest Edition), or, if such rate is not then so published on at least a
weekly basis, the interest rate announced by Chase Manhattan Bank (or its
successor), from time to time, as its Base Rate (or prime lending rate), from
the date those amounts were required to have been paid or reimbursed to the
Employee until those amounts are finally and fully paid or reimbursed; provided,
however, that in no event shall the amount of interest contracted for, charged
or received hereunder exceed the maximum non-usurious amount of interest allowed
by applicable law; provided, further, that if the Executive is not the
prevailing party in any such contest, then he shall, upon the conclusion
thereof, repay to the Company any amounts that were previously advanced pursuant
to this sentence by the Company as payment of legal fees and expenses.

          (b) If there shall be any dispute between the Company and the
Executive concerning (i) in the event of any termination of the Executive's
employment by the Company, whether such termination was for Cause or Disability,
or (ii) in the event of any termination of employment by the Executive, whether
Good Reason existed or whether such termination occurred during a Window Period,
then, unless and until there is a final, nonappealable judgment by a court of
competent jurisdiction declaring that such termination was for Cause or
Disability or that the determination by the Executive of the existence of Good
Reason was not made in good faith or that the termination by the Executive did
not occur during a Window Period, the Company shall pay all amounts, and provide
all benefits, to the Executive and/or the Executive's family or other
beneficiaries, as the case may be, that the Company would be required to pay or
provide pursuant to Section 4(a) hereof as though such termination were by the
Company without Cause or by the Executive with Good Reason or during a Window
Period; provided, however, that the Company 

                                       11
<PAGE>
 
shall not be required to pay any disputed amounts pursuant to this paragraph
except upon receipt of an undertaking by or on behalf of the Executive to repay
all such amounts to which the Executive is ultimately adjudged by such court not
to be entitled.

          7.  Certain Additional Payments by the Company.
              ------------------------------------------- 

          (a) Anything in this Agreement to the contrary notwithstanding, in the
event it shall be determined that any payment or distribution to or for the
benefit of the Executive (whether paid or payable or distributed or
distributable pursuant to the terms of this Agreement or otherwise, but
determined without regard to any additional payments required under this Section
7 (a "Payment") would be subject to the excise tax imposed by Section 4999 of
the Code or any interest or penalties are incurred by the Executive with respect
to such excise tax (such excise tax, together with any such interest and
penalties, are hereinafter collectively referred to as the "Excise Tax"), then
the Executive shall be entitled to receive an additional payment (a "Gross-Up
Payment") in an amount such that after payment by the Executive of all taxes
(including any interest or penalties imposed with respect to such taxes),
including, without limitation, any income taxes (and any interest and penalties
imposed with respect thereto) and Excise Tax imposed upon the Gross-Up Payment,
the Executive retains an amount of the Gross-Up Payment equal to the Excise Tax
imposed upon the Payments.

          (b) Subject to the provisions of Section 7(c), all determinations
required to be made under this Section 7, including whether and when Gross-Up
Payment is required and the amount of such Gross-Up Payment and the assumptions
to be utilized in arriving at such determination, shall be made by Deloitte &
Touche LLP (the "Accounting Firm"); provided, however, that the Accounting Firm
shall not determine that no Excise Tax is payable by the Executive unless it
delivers to the Executive a written opinion (the "Accounting Opinion") that
failure to report the Excise Tax on the Executive's applicable federal income
tax return would not result in the imposition of a negligence or similar
penalty. In the event that by Deloitte & Touche LLP has served, at any time
during the two years immediately preceding a Change in Control Date, as
accountant or auditor for the individual, entity or group that is involved in
effecting or has any material interest in the Change in Control, the Executive
shall appoint another nationally recognized accounting firm to make the
determinations and perform the other functions specified in this Section 7
(which accounting firm shall then be referred to as the Accounting Firm
hereunder).  All fees and expenses of the Accounting Firm shall be borne solely
by the Company.  Within 15 business days of the receipt of notice from the
Executive that there has been a Payment, or such earlier time as is requested by
the Company, the Accounting Firm shall make all determinations required under
this Section 7, shall provide to the Company and the Executive a written report
setting forth such determinations, together with detailed supporting
calculations, and, if the Accounting Firm determines that no Excise Tax is
payable, shall deliver the Accounting Opinion to the Executive.  Any Gross-Up
Payment, as determined pursuant to this Section 7, shall be paid by the Company
to the Executive within five days of the receipt of the Accounting Firm's
determination.  Subject to the remainder of this Section 7, any determination by
the Accounting Firm shall be binding upon the Company and the Executive.  As a
result of the uncertainty in the application of Section 4999 of the 

                                       12
<PAGE>
 
Code at the time of the initial determination by the Accounting Firm hereunder,
it is possible that Gross-Up Payments which will not have been made by the
Company should have been made ("Underpayment"), consistent with the calculations
required to be made hereunder. In the event that it is ultimately determined in
accordance with the procedures set forth in Section 7(c) that the Executive is
required to make a payment of any Excise Tax, the Accounting Firm shall
determine the amount of the Underpayment that has occurred and any such
Underpayment shall be promptly paid by the Company to or for the benefit of the
Executive.

          (c) The Executive shall notify the Company in writing of any claims by
the Internal Revenue Service that, if successful, would require the payment by
the Company of the Gross-Up Payment.  Such notification shall be given as soon
as practicable but no later than 30 days after the Executive actually receives
notice in writing of such claim and shall apprise the Company of the nature of
such claim and the date on which such claim is requested to be paid; provided,
however, that the failure of the Executive to notify the Company of such claim
(or to provide any required information with respect thereto) shall not affect
any rights granted to the Executive under this Section 7 except to the extent
that the Company is materially prejudiced in the defense of such claim as a
direct result of such failure.  The Executive shall not pay such claim prior to
the expiration of the 30-day period following the date on which he gives such
notice to the Company (or such shorter period ending on the date that any
payment of taxes with respect to such claim is due).  If the Company notifies
the Executive in writing prior to the expiration of such period that it desires
to contest such claim, the Executive shall:

     (i) give the Company any information reasonably requested by the Company
relating to such claim;

     (ii) take such action in connection with contesting such claim as the
Company shall reasonably request in writing from time to time, including,
without limitation, accepting legal representation with respect to such claim by
an attorney selected by the Company and reasonably acceptable to the Executive;

     (iii)  cooperate with the Company in good faith in order effectively to
contest such claim; and

     (iv) if the Company elects not to assume and control the defense of such
claim, permit the Company to participate in any proceedings relating to such
claim;

provided, however, that the Company shall bear and pay directly all costs and
expenses (including additional interest and penalties) incurred in connection
with such contest and shall indemnify and hold the Executive harmless, on an
after-tax basis, for any Excise Tax or income tax (including interest and
penalties with respect thereto) imposed as a result of such representation and
payment of costs and expenses.  Without limitation on the foregoing provisions
of this Section 7(c), the Company shall have the right, at its sole option, to
assume the defense of and control all proceedings in connection with such
contest, in which case it may pursue or forego any and all administrative

                                       13
<PAGE>
 
appeals, proceedings, hearings and conferences with the taxing authority in
respect of such claim, and may either direct the Executive to pay the tax
claimed and sue for a refund or contest the claim in any permissible manner, and
the Executive agrees to prosecute such contest to a determination before any
administrative tribunal, in a court of initial jurisdiction and in one or more
appellate courts, as the Company shall determine; provided, however, that if the
Company directs the Executive to pay such claim and sue for a refund, the
Company shall advance the amount of such payment to the Executive, on an
interest-free basis, and shall indemnify and hold the Executive harmless, on an
after-tax basis, from any Excise Tax or income tax (including interest or
penalties with respect thereto) imposed with respect to such advance or with
respect to any imputed income with respect to such advance; and further
provided, that any extension of the statute of limitations relating to payment
of taxes for the taxable year of the Executive with respect to which such
contested amount is claimed to be due is limited solely to such contested
amount. Furthermore, the Company's right to assume the defense of and control
the contest shall be limited to issues with respect to which a Gross-Up Payment
would be payable hereunder and the Executive shall be entitled to settle or
contest, as the case may be, any other issue raised by the Internal Revenue
Service or any other taxing authority.

          (d) If, after the receipt by the Executive of an amount advanced by
the Company pursuant to Section 7(c) the Executive becomes entitled to receive
any refund with respect to such claim, the Executive shall (subject to the
Company's complying with the requirements of Section 7(c)) promptly pay to the
Company the amount of such refund (together with any interest paid or credited
thereon after taxes applicable thereto).  If, after the receipt by the Executive
of an amount advanced by the Company pursuant to Section 7(c) a determination is
made that the Executive shall not be entitled to any refund with respect to such
claim, and the Company does not notify the Executive in writing of its intent to
contest such denial of refund prior to the expiration of 30 days after such
determination, then such advance shall be forgiven and shall not be required to
be repaid and the amount of such advance shall offset, to the extent thereof,
the amount of Gross-Up Payment required to be paid.

          8.  Confidential Information.  The Executive shall hold in a fiduciary
capacity for the benefit of the Company all secret or confidential information,
knowledge or data relating to the Company or any of its affiliated companies,
and their respective businesses, which shall have been obtained by the Executive
during the Executive's employment by the Company or any of its affiliated
companies and which shall not be or become public knowledge (other than by acts
by the Executive or representatives of the Executive in violation of this
Agreement) (referred to herein as "Confidential Information").  After
termination of the Executive's employment with the Company, the Executive shall
not, without the prior written consent of the Company or as may otherwise be
required by law or legal process, communicate or divulge any such information,
knowledge or data to anyone other than the Company and those designated by it.
In no event shall an asserted violation of the provisions of this Section 8
constitute a basis for deferring or withholding any amounts otherwise payable to
the Executive under this Agreement.  Also, within 10 days of the termination of
Executive's employment for any reason, Executive shall return to Company all
documents and 

                                       14
<PAGE>
 
other tangible items of or containing Company information which are in
Executive's possession, custody or control.

          9.  Change of Control.
              ------------------ 

          As used in this Agreement, the terms set forth below shall have the
following respective meanings:

          "Affiliate" shall have the meaning ascribed to such term in Rule 12b-2
of the General Rules and Regulations under the Exchange Act, as in effect on the
date of this Agreement.

          "Associate" shall mean, with reference to any Person, (a) any
corporation, firm, partnership, association, unincorporated organization or
other entity (other than the Company or a subsidiary of the Company) of which
such Person is an officer or general partner (or officer or general partner of a
general partner) or is, directly or indirectly, the Beneficial Owner of 10% or
more of any class of equity securities, (b) any trust or other estate in which
such Person has a substantial beneficial interest or as to which such Person
serves as trustee or in a similar fiduciary capacity and (c) any relative or
spouse of such Person, or any relative of such spouse, who has the same home as
such Person.

          "Beneficial Owner" shall mean, with reference to any securities, any
Person if:

     (a) such Person or any of such Person's Affiliates and Associates, directly
or indirectly, is the "beneficial owner" of (as determined pursuant to Rule 13d-
3 of the General Rules and Regulations under the Exchange Act, as in effect on
the date of this Agreement) such securities or otherwise has the right to vote
or dispose of such securities, including pursuant to any agreement, arrangement
or understanding (whether or not in writing); provided, however, that a Person
shall not be deemed the "Beneficial Owner" of, or to "beneficially own," any
security under this subsection (a) as a result of an agreement, arrangement or
understanding to vote such security if such agreement, arrangement or
understanding:  (i) arises solely from a revocable proxy or consent given in
response to a public (i.e., not including a solicitation exempted by Rule 14a-
2(b)(2) of the General Rules and Regulations under the Exchange Act) proxy or
consent solicitation made pursuant to, and in accordance with, the applicable
provisions of the General Rules and Regulations under the Exchange Act and (ii)
is not then reportable by such Person on Schedule 13D under the Exchange Act (or
any comparable or successor report);

     (b) such Person or any of such Person's Affiliates and Associates, directly
or indirectly, has the right or obligation to acquire such securities (whether
such right or obligation is exercisable or effective immediately or only after
the passage of time or the occurrence of an event) pursuant to any agreement,
arrangement or understanding (whether or not in writing) or upon the exercise of
conversion rights, exchange rights, other rights, warrants or options, or
otherwise; provided, however, that a Person shall not be deemed the 

                                       15
<PAGE>
 
Beneficial Owner of, or to "beneficially own," (i) securities tendered pursuant
to a tender or exchange offer made by such Person or any of such Person's
Affiliates or Associates until such tendered securities are accepted for
purchase or exchange or (ii) securities issuable upon exercise of Exempt Rights;
or

     (c) such Person or any of such Person's Affiliates or Associates (i) has
any agreement, arrangement or understanding (whether or not in writing) with any
other Person (or any Affiliate or Associate thereof) that beneficially owns such
securities for the purpose of acquiring, holding, voting (except as set forth in
the proviso to subsection (a) of this definition) or disposing of such
securities or (ii) is a member of a group (as that term is used in Rule 13d-5(b)
of the General Rules and Regulations under the Exchange Act) that includes any
other Person that beneficially owns such securities;

provided, however, that nothing in this definition shall cause a Person engaged
in business as an underwriter of securities to be the Beneficial Owner of, or to
"beneficially own," any securities acquired through such Person's participation
in good faith in a firm commitment underwriting until the expiration of 40 days
after the date of such acquisition.  For purposes hereof, "voting" a security
shall include voting, granting a proxy, consenting or making a request or demand
relating to corporate action (including, without limitation, a demand for a
stockholder list, to call a stockholder meeting or to inspect corporate books
and records) or otherwise giving an authorization (within the meaning of Section
14(a) of the Exchange Act) in respect of such security.

          The terms "beneficially own" and "beneficially owning" shall have
meanings that are correlative to this definition of the term "Beneficial Owner."

          "Change of Control" shall mean any of the following occurring on or
after the Agreement Effective Date except that the transactions contemplated by
the Combination Agreement dated as of December 3, 1996, by and among the
Company, Edge Petroleum Corporation, a Texas corporation, Edge Mergeco, Inc.,
Gulfedge Limited Partnership, Edge Group II Limited Partnership and Edge Group
Partnership shall not constitute a Change of Control:

     (a) any Person (other than an Exempt Person) shall become the Beneficial
Owner of 40% or more of the shares of Common Stock then outstanding or 40% or
more of the combined voting power of the Voting Stock of the Company then
outstanding; provided, however, that no Change of Control shall be deemed to
occur for purposes of this subsection (a) if such Person shall become a
Beneficial Owner of 40% or more of the shares of Common Stock or 40% or more of
the combined voting power of the Voting Stock of the Company solely as a result
of (i) an Exempt Transaction or (ii) an acquisition by a Person pursuant to a
reorganization, merger or consolidation, if, following such reorganization,
merger or consolidation, the conditions described in clauses (i), (ii) and (iii)
of subsection (c) of this definition are satisfied;

                                       16
<PAGE>
 
     (b) individuals who, as of the Agreement Effective Date, constitute the
Board (the "Incumbent Board") cease for any reason to constitute at least a
majority of the Board; provided, however, that any individual becoming a
director subsequent to the Agreement Effective Date whose election, or
nomination for election by the Company's shareholders, was approved by a vote of
at least a majority of the directors then comprising the Incumbent Board shall
be considered as though such individual were a member of the Incumbent Board;
provided, further, that there shall be excluded, for this purpose, any such
individual whose initial assumption of office occurs as a result of any actual
or threatened election contest that is subject to the provisions of Rule 14a-11
under the Exchange Act;

     (c) approval by the shareholders of the Company of a reorganization, merger
or consolidation, in each case, unless, following such reorganization, merger or
consolidation, (i) more than 85% of the then outstanding shares of common stock
of the corporation resulting from such reorganization, merger or consolidation
and the combined voting power of the then outstanding Voting Stock of such
corporation beneficially owned, directly or indirectly, by all or substantially
all of the Persons who were the Beneficial Owners of the outstanding Common
Stock immediately prior to such reorganization, merger or consolidation in
substantially the same proportions as their ownership, immediately prior to such
reorganization, merger or consolidation, of the outstanding Common Stock, (ii)
no Person (excluding any Exempt Person or any Person beneficially owning,
immediately prior to such reorganization, merger or consolidation, directly or
indirectly, 40% or more of the Common Stock then outstanding or 40% or more of
the combined voting power of the Voting Stock of the Company then outstanding)
beneficially owns, directly or indirectly, 40% or more of the then outstanding
shares of common stock of the corporation resulting from such reorganization,
merger or consolidation or the combined voting power of the then outstanding
Voting Stock of such corporation and (iii) at least a majority of the members of
the board of directors of the corporation resulting from such reorganization,
merger or consolidation were members of the Incumbent Board at the time of the
execution of the initial agreement or initial action by the Board providing for
such reorganization, merger or consolidation; or

     (d) approval by the shareholders of the Company of (i) a complete
liquidation or dissolution of the Company unless such liquidation or dissolution
is approved as part of a plan of liquidation and dissolution involving a sale or
disposition of all or substantially all of the assets of the Company to a
corporation with respect to which, following such sale or other disposition, all
of the requirements of clauses (ii)(A), (B) and (C) of this subsection (d) are
satisfied, or (ii) the sale or other disposition of all or substantially all of
the assets of the Company, other than to a corporation, with respect to which,
following such sale or other disposition, (A) more than 85% of the then
outstanding shares of common stock of such corporation and the combined voting
power of the Voting Stock of such corporation is then beneficially owned,
directly or indirectly, by all or substantially all of the Persons who were the
Beneficial Owners of the outstanding Common Stock immediately prior to such sale
or other disposition in substantially the same proportion as their ownership,
immediately prior to such sale or other disposition, of the outstanding Common
Stock, (B) no Person (excluding any Exempt Person and any Person beneficially
owning, immediately prior 

                                       17
<PAGE>
 
to such sale or other disposition, directly or indirectly, 40% or more of the
Common Stock then outstanding or 40% or more of the combined voting power of the
Voting Stock of the Company then outstanding) beneficially owns, directly or
indirectly, 40% or more of the then outstanding shares of common stock of such
corporation and the combined voting power of the then outstanding Voting Stock
of such corporation and (C) at least a majority of the members of the board of
directors of such corporation were members of the Incumbent Board at the time of
the execution of the initial agreement or initial action of the Board providing
for such sale or other disposition of assets of the Company.

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

          "Exempt Person" shall mean the Company, any subsidiary of the Company,
any employee benefit plan of the Company or any subsidiary of the Company, and
any Person organized, appointed or established by the Company for or pursuant to
the terms of any such plan.

          "Exempt Rights" shall mean any rights to purchase shares of Common
Stock or other Voting Stock of the Company if at the time of the issuance
thereof such rights are not separable from such Common Stock or other Voting
Stock (i.e., are not transferable otherwise than in connection with a transfer
of the underlying Common Stock or other Voting Stock) except upon the occurrence
of a contingency, whether such rights exist as of the Agreement Effective Date
or are thereafter issued by the Company as a dividend on shares of Common Stock
or other Voting Securities or otherwise.

          "Exempt Transaction" shall mean an increase in the percentage of the
outstanding shares of Common Stock or the percentage of the combined voting
power of the outstanding Voting Stock of the Company beneficially owned by any
Person solely as a result of a reduction in the number of shares of Common Stock
then outstanding due to the repurchase of Common Stock or Voting Stock by the
Company, unless and until such time as (a) such Person or any Affiliate or
Associate of such Person shall purchase or otherwise become the Beneficial Owner
of additional shares of Common Stock constituting 1% or more of the then
outstanding shares of Common Stock or additional Voting Stock representing 1% or
more of the combined voting power of the then outstanding Voting Stock, or (b)
any other Person (or Persons) who is (or collectively are) the Beneficial Owner
of shares of Common Stock constituting 1% or more of the then outstanding shares
of Common Stock or Voting Stock representing 1% or more of the combined voting
power of the then outstanding Voting Stock shall become an Affiliate or
Associate of such Person.

          "Person" shall mean any individual, firm, corporation, partnership,
association, trust, unincorporated organization or other entity.

          "Voting Stock" shall mean, with respect to a corporation, all
securities of such corporation of any class or series that are entitled to vote
generally in the election of directors of such 

                                       18
<PAGE>
 
corporation (excluding any class or series that would be entitled so to vote by
reason of the occurrence of any contingency, so long as such continency has not
occurred).

          10.  Covenant Not to Compete.
               ------------------------ 

          (a) Executive recognizes that in each of the highly competitive
businesses in which the Company is engaged, personal contact is of primary
importance in securing new customers and in retaining the accounts and goodwill
of present customers and protecting the business of the Company.  The Executive,
therefore, agrees that during the Employment Period and, if the Date of
Termination occurs by reason of the Executive terminating his employment for
reasons other than Disability or Good Reason and other than during a Window
Period, for a period of two years after the Date of Termination, he will not,
either within 100 miles of any geographic location with respect to which he has
devoted substantial attention to the material business interests of the Company
(other than the Company's home office) or any of its affiliated companies or
with respect to any immediate geologic trends in which the Company or any of its
affiliated companies is active as of the Date of Termination without regard, in
either case, to whether the Executive has worked at such location (the "Relevant
Geographic Area"), with respect to only the Relevant Geographic Area, (i) accept
employment or render service to any person that is engaged in a business
directly competitive with the business then engaged in by the Company or any of
its affiliated companies or (ii) enter into or take part in or lend his name,
counsel or assistance to any business, either as proprietor, principal,
investor, partner, director, officer, executive, consultant, advisor, agent,
independent contractor, or in any other capacity whatsoever, for any purpose
that would be competitive with the business of the Company or any of its
affiliated companies (all of the foregoing activities are collectively referred
to as the "Prohibited Activity").

          (b) In addition to all other remedies at law or in equity which the
Company may have for breach of a provision of this Section 10 by the Executive,
it is agreed that in the event of any breach or attempted or threatened breach
of any such provision, the Company shall be entitled, upon application to any
court of proper jurisdiction, to a temporary restraining order or preliminary
injunction (without the necessity of (i) proving irreparable harm, (ii)
establishing that monetary damages are inadequate or (iii) posting any bond with
respect thereto) against the Executive prohibiting such breach or attempted or
threatened breach by proving only the existence of such breach or attempted or
threatened breach.  If the provisions of this Section 10 should ever be deemed
to exceed the time, geographic or occupational limitations permitted by the
applicable law, the Executive and the Company agree that such provisions shall
be and are hereby reformed to the maximum time, geographic or occupational
limitations permitted by the applicable law.

          (c) The covenants of the Executive set forth in this Section 10 are
independent of and severable from every other provision of this Agreement; and
the breach of any other provision of this Agreement by the Company or the breach
by the Company of any other agreement between the Company and the Executive
shall not affect the validity of the provisions of this Section 10 or constitute
a defense of the Executive in any suit or action brought by the Company to
enforce any of the provisions of this Section 10 or seek any relief for the
breach thereof by Executive.

                                       19
<PAGE>
 
          (d) The Executive acknowledges, agrees and stipulates that:  (i) the
terms and provisions of this Agreement are reasonable and constitute an
otherwise enforceable agreement to which the terms and provisions of this
Section 10 are ancillary or a part of as contemplated by Tex. Bus. & Com. Code
Ann. (S)(S) 15.50-15.52; (ii) the consideration provided by the Company under
this Agreement is not illusory; and (iii) the consideration given by the Company
under this Agreement, including, without limitation, the provision by the
Company of Confidential Information to the Executive as contemplated by Section
8, gives rise to the Company's interest in restraining and prohibiting the
Executive from engaging in the Prohibited Activity within the Relevant
Geographic Area as provided under this Section 10, and the Executive's covenant
not to engage in the Prohibited Activity within the Relevant Geographic Area
pursuant to this Section 10 is designed to enforce the Executive's consideration
(or return promises), including, without limitation, the Executive's promise to
not disclose Confidential Information under this Agreement.

          11.  Successors.
               ---------- 

          (a) This Agreement is personal to the Executive and without the prior
written consent of the Company shall not be assignable by the Executive
otherwise than by will or the laws of descent and distribution.  This Agreement
shall inure to the benefit of and be enforceable by the Executive's heirs,
executors and other legal representatives.

          (b) This Agreement shall inure to the benefit of and be binding upon
the Company and may only be assigned to a successor described in Section 11(c).

          (c) The Company will require any successor (whether direct or
indirect, by purchase, merger, consolidation or otherwise) to all or
substantially all of the business and/or assets of the Company to assume
expressly and agree to perform this Agreement in the same manner and to the same
extent that the Company would be required to perform it if no such succession
had taken place.  As used in this Agreement, "Company" shall mean the Company as
hereinbefore defined and any successor to its business and/or assets as
aforesaid which assumes and agrees to perform this Agreement by operation of
law, or otherwise.

          12.  Miscellaneous.
               ------------- 

          (a) This Agreement shall be governed by and construed in accordance
with the laws of the State of Texas, without reference to principles of conflict
of laws that would require the application of the laws of any other state or
jurisdiction.

          (b) The captions of this Agreement are not part of the provisions
hereof and shall have no force or effect.

          (c) This Agreement may not be amended or modified otherwise than by a
written agreement executed by the parties hereto or their respective successors
and heirs, executors and other legal representatives.

                                       20
<PAGE>
 
          (d) All notices and other communications hereunder shall be in writing
and shall be given, if by the Executive to the Company, by telecopy or facsimile
transmission at the telecommunications number set forth below and, if by either
the Company or the Executive, either by hand delivery to the other party or by
registered or certified mail, return receipt requested, postage prepaid,
addressed as follows:

           If to the Executive:
           ------------------- 

           John E. Calaway
           Texaco Heritage Plaza
           1111 Bagby, Suite 2100
           Houston, Texas 77002

           If to the Company:
           ----------------- 

           Edge Petroleum Corporation
           Texaco Heritage Plaza
           1111 Bagby, Suite 2100
           Houston, Texas 77002
           Telecommunications Number:  (713) 654-8960
           Attention: Corporate Secretary

or to such other address as either party shall have furnished to the other in
writing in accordance herewith.  Notice and communications shall be effective
when actually received by the addressee.

          (e) The invalidity or unenforceability of any provision of this
Agreement shall not affect the validity or enforceability of any other provision
of this Agreement.

          (f) The Company may withhold from any amounts payable under this
Agreement such federal, state or local taxes as shall be required to be withheld
pursuant to any applicable law or regulation.

          (g) The Executive's or the Company's failure to insist upon strict
compliance with any provision hereof or any other provision of this Agreement or
the failure to assert any right the Executive or the Company may have hereunder,
including, without limitation, the right of the Executive to terminate
employment for Good Reason or during a Window Period pursuant to Section 3(c) of
this Agreement, shall not be deemed to be a waiver of such provision or right or
any other provision or right of this Agreement.

          (h) This agreement contains the complete and total understanding of
the parties concerning the subject matter hereof and expressly supersedes any
previous agreement between the parties relating to the subject matter hereof as
well as any agreement between Executive and Edge Petroleum Corporation, a Texas
corporation.

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<PAGE>
 
          (i) This Agreement shall become effective as of the date on which the
Company first receives payment for shares of its Common Stock that it sells
pursuant to a registration statement filed under the Securities Act of 1933 (the
"Agreement Effective Date").

          IN WITNESS WHEREOF, the Executive has hereunto set his hand and,
pursuant to the authorization from its Board of Directors, the Company has
caused these presents to be executed in its name on its behalf, all as of the
day and year first above written.

                                          EDGE PETROLEUM CORPORATION


                                              /s/ JAMES D. CALAWAY
                                          By:____________________________
                                             James D. Calaway


                                              /s/ JOHN E. CALAWAY
                                          By:____________________________
                                             John E. Calaway

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