<PAGE>
 
                                                                   EXHIBIT 10.25

                            SUPPLEMENTAL AGREEMENT
                            ----------------------


     THIS SUPPLEMENTAL AGREEMENT (the "Agreement") is made and entered into as
of the 17th day of November, 1998, by and between D. JOSEPH CORR ("Corr") and
AIRTRAN HOLDINGS, INC., a Nevada corporation (the "Company").

                             W I T N E S S E T H:
                             - - - - - - - - - - 


     WHEREAS, the parties hereto desire to state herein the continuing rights,
duties and obligations between themselves following the termination of Corr's
employment as President and Chief Executive Officer of the Company;

     NOW, THEREFORE, in consideration of the mutual promises of the parties
hereto and of the mutual benefits to be gained by the performance thereof, and
for other good and valuable consideration, the receipt, adequacy and sufficiency
of which are hereby acknowledged, the parties hereto, intending to be legally
bound hereby, do hereby agree as follows:

     1.   Effective Date.  This Agreement shall not become effective until the
          --------------                                                      
Effective Date set forth in Item 3A below and shall have no force and effect
until such time.

     2.   Termination of Prior Agreements.
          ------------------------------- 

          A.   Except as provided in Paragraph B below, this Agreement shall as
of the Effective Date contain all of the covenants and agreements between the
parties hereto with respect to the subject matter hereof.  This Agreement shall
as of the Effective Date supersede any and all other agreements, either oral or
in writing between the parties hereto with respect to the subject matter hereof,
including but not limited to that certain Employment Agreement dated as of
January 1, 1998, by and between Corr and the Company (the "Employment
Agreement").

          B.   Notwithstanding the foregoing, that certain Stock Option
Agreement dated January 6, 1997 between Corr and the Company and that certain
Stock Option Agreement dated November 25, 1997 between Corr and the Company, as
such agreements are being amended simultaneously herewith, shall remain in full
force and effect to govern the terms of Corr's stock options in the Company.

     3.   President/CEO Status.
          -------------------- 

          A.   Corr shall continue to serve as President and Chief Executive
Officer of the Company until such date (the "Effective Date") as shall be
identified by the Board of Directors of the Company by written notice to Corr.
The Effective Date shall not be earlier than November 18, 1998.

          B.   As of the Effective Date, Corr hereby resigns as President and
Chief Executive Officer and as a Director of the Company.  As of the Effective
Date, Corr does also hereby resign as a director and officer of each subsidiary
of the Company, including, but not limited to, AirTran Airways, Inc., AirTran
Airlines, Inc. and ValuJet Investment Corp.
<PAGE>
 
          C.   After the Effective Date, Corr agrees to use good faith efforts
to cooperate with the successor chief executive officer in order to provide for
a smooth transition for the Company.

     4.   Compensatory Payments from the Company.
          -------------------------------------- 

          A.   Corr shall be entitled to receive his usual base salary from the
Company (at the rate of $25,000 per month) for services rendered by Corr up to
and until the Effective Date.

          B.   Upon the Effective Date, the Company shall pay to Corr a lump sum
severance payment of $300,000.

          C.   Corr hereby acknowledges that except as expressly set out in this
Agreement, Corr has heretofore received all compensation to which he was
entitled from the Company or any subsidiary of the Company pursuant to the
Employment Agreement or otherwise for all periods through and including the
Effective Date.

          D.   Corr shall be responsible for all social security, federal and
state withholding taxes and any other such taxes required by governmental
authority with respect to the payments from the Company to Corr under this Item
4.

     5.   Stock Options.
          ------------- 

          A.   The parties acknowledge that Corr has the following options to
purchase stock in the Company:  options to purchase 450,000 shares at $7.125 per
share under a Stock Option Agreement dated January 6, 1997 (the "1996 Options")
and options to purchase 150,000 shares at $5.50 per share under a Stock Option
Agreement dated November 25, 1997 (the "1997 Options").

          B.   The parties acknowledge that: (i) as of the Effective Date, Corr
will have the vested right to exercise all of the 1996 Options and 100,000 of
the 1997 Options;  (ii) Corr shall have the right to exercise his vested options
at any time prior to the date that is five (5) years after the Effective Date;
and (iii) in the event of Corr's death prior to the exercise of such stock
options, Corr's personal representative shall have the right to exercise Corr's
vested stock options at any time prior to the earlier of the date that is one
(1) year after Corr's death or the date that is five (5) years after the
Effective Date.

          C.   The parties agree to execute amendments to Corr's Stock Option
Agreements in the form attached hereto as Exhibits "A" and "B" in order to
effectuate the provisions of this Item 5.

     6.   Continuing Health Insurance/Flight Passes.
          ----------------------------------------- 

          A.   Corr and his wife shall have the right during their lifetimes to
continuing coverage in the Company's (or its successor's) health insurance plan
in effect from time to time.  Such participation shall be at Corr's cost, not to
exceed the COBRA (or equivalent) premium that would be chargeable with respect
to such coverage.

                                      -2-
<PAGE>
 
          B.   Corr and his wife shall have lifetime pass privileges on Company
flights, consistent with the most favorable pass privileges available to any
Company executives as in effect from time to time.

     7.   Indemnification of Corr.  Except as provided below, the Company shall
          -----------------------                                              
indemnify Corr in the event he is made a party to a proceeding because he is or
was a director or officer of the Company against liability incurred by him in
the proceeding if he acted in good faith and in a manner he believed to be in or
not opposed to the best interests of the Company and, in the case of any
criminal proceeding, he had no reasonable cause to believe his conduct was
unlawful.  The Company shall not indemnify Corr under this paragraph in
connection with a proceeding by or in the right of the Company in which Corr is
adjudged liable to the Company, unless and only to the extent the court in which
the proceeding is brought or other court of competent jurisdiction determines
upon application that in view of all circumstances of the case, Corr is fairly
and reasonably entitled to indemnity for such expenses as the court deems
proper. Indemnification permitted under this paragraph in connection with a
proceeding is limited to liability and expenses actually and reasonably incurred
in connection with the proceeding.

     8.   Mutual Releases.
          --------------- 

          A.   The Company, on behalf of itself, its agents, successors and
assigns (collectively referred to in this Paragraph as the "Releasors"), do
hereby release, remise and forever discharge Corr and his agents, personal
representatives, heirs, legal representatives, successors and assigns
(collectively referred to in this Paragraph as the "Releasees" but expressly
excluding the Releasors) of and from any and all actions, suits, debts, dues,
accounts, bonds, covenants, contracts, agreements, judgments, liens, claims,
demands and liabilities of whatsoever type or description and no matter how
arising, in law or in equity, known or unknown, which the Releasors ever had,
now have or may hereafter have against the Releasees for or by reason of any
cause, matter or thing whatsoever from the beginning of the world to the
Effective Date; provided, however, that the provisions of this Paragraph shall
not extend to (i) the obligations of the Releasees under and pursuant to this
Agreement, or (ii) any costs, expenses or liabilities incurred by Releasors
which arise out of or relate to any acts or omissions by Corr which are illegal
or unethical, including but not limited to fraud or sexual harassment, or (iii)
any acts or omissions after the Effective Date hereof.

          B.   Corr, on behalf of himself, his agents, personal representatives,
heirs, legal representatives, successors and assigns (collectively referred to
in this Paragraph as the "Releasors") does hereby release, remise and forever
discharge the Company and its agents, officers, directors, shareholders,
employees, personal representatives, heirs, legal representatives, successors,
subsidiaries and assigns (collectively referred to in this Paragraph as the
"Releasees" but expressly excluding the Releasors) of and from any and all
actions, suits, debts, dues, accounts, bonds, covenants, contracts, agreements,
judgments, liens, claims, demands and liabilities of whatsoever type or
description and no matter how arising, in law or in equity, known or unknown,
which the Releasors ever had, now have or may hereafter have against the
Releasees for or by reason of any cause, matter or thing whatsoever from the
beginning of the world to the Effective Date; provided, however, that the
provisions of this Paragraph shall not extend to (i) the obligations of the
Releasees under and pursuant to this Agreement, or (ii) any acts or omissions
after the Effective Date hereof.

                                      -3-
<PAGE>
 
     9.   Further Assurances.  At any time and from time to time after the date
          ------------------                                                   
of this Agreement, upon request of any party hereto and without the payment of
any further consideration, another party hereto shall duly execute, acknowledge
and deliver all such further assignments, conveyances and other instruments of
transfer and other documents, and will take such other action, consistent with
the terms of this Agreement, as reasonably may be requested for the purposes of
consummating the transactions contemplated hereby.

     10.  Waiver.  Failure to insist upon strict compliance with any of the
          ------                                                           
terms, covenants or conditions hereof shall not be deemed a waiver of such
terms, covenants or conditions, nor shall any waiver or relinquishment of any
right or power hereunder, at any one time or more times, be deemed a waiver or
relinquishment of such right or power at any other time or times.

     11.  Specific Performance - Breach.  All parties acknowledge that a breach
          -----------------------------                                        
of this Agreement will result in irreparable and continuing damage for which
there may be no adequate remedy at law.  Therefore, in addition to any other
remedy afforded by law, any breach or threatened breach of this Agreement shall
be subject to specific performance by injunction or any other equitable remedies
of any court of competent jurisdiction.

     12.  Transaction Expenses.  All fees and expenses incurred by the parties
          --------------------                                                
in connection with the negotiation of this Agreement and the consummation of the
transactions contemplated herein shall be paid and borne by the respective party
incurring such cost.

     13.  Miscellaneous.  This Agreement shall be governed by the laws of the
          -------------                                                      
State of Nevada.  No amendment or modification of this Agreement shall be valid
or binding upon any party unless made in writing and duly signed by all parties.
This Agreement may be executed in one or more counterparts, each of which shall
be deemed to be an original, but all of which together shall constitute one and
the same instrument.  The rights and obligations of a party under this Agreement
shall not be subject to assignment or alienation without the prior written
consent of the other party.  The losing party in any action brought to enforce
the terms of this Agreement shall pay the attorney's fees and all other costs
incurred by the prevailing party in any such action.  This Agreement shall be
binding upon and shall inure to the benefit of the parties hereto and their
respective heirs, legal representatives, and permitted successors and assigns.
All representations, warranties, covenants and agreements made by a party to
this Agreement or pursuant hereto shall survive the closing of the transactions
contemplated hereby and shall be actionable at any time after said closing.

     14.  Notices.  Any notice required or permitted to be given pursuant to
          -------                                                           
this Agreement shall be sufficiently given when personally delivered (with
written acknowledgment of receipt of such personal delivery) or mailed by
certified or registered mail, return receipt requested, postage prepaid:

          To the Company:            9955 AirTran Boulevard
                                     Orlando, Florida 32827
                                     (407) 251-5944
                                     Attn: President

                                      -4-
<PAGE>
 
          To Corr:                   _________________________

                                     _________________________

                                     _________________________


or at such other address as any of such parties to be given notice shall
designate by written notice to the other parties.

     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the day and year first above written.


                                  ___________________________(SEAL)
                                  D. JOSEPH CORR



                                  AIRTRAN HOLDINGS, INC.


                                  By: /s/ Robert D. Swenson
                                     ------------------------------
                                      Robert D. Swenson
                                  Title: Chairman of the Board
 
                                              (CORPORATE SEAL)

                                      -5-
<PAGE>
 
                                  EXHIBIT "A"


                                 AMENDMENT TO
                            STOCK OPTION AGREEMENT

     THIS IS AN AMENDMENT (the "Amendment") to that certain Stock Option
Agreement dated January 6, 1997 (the "Agreement") between AIRTRAN HOLDINGS,
INC., a Nevada corporation formerly known as ValuJet, Inc.(the "Company")
and D. JOSEPH CORR (the"Optionee"). Under the Agreement, Optionee was granted
options to purchase 450,000 shares at $7.125 per share.

     In consideration of Optionee's past and future employment with the
Company and its subsidiaries and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties 
acknowledge and agree as follows:

1.   Item 2C of the Agreement is herby amended to read as follows:

          "C.  Options granted under this Agreement shall constitute 
     nonqualified stock options."

2.   The vesting schedule contained in Item 5A of the Agreement is hereby
     amended to read as follows:

                               "Vesting Schedule
                               -----------------
     
               As of                    Number of Option Shares Exercisable
               -----                    -----------------------------------
       
               The date hereof                    300,000
               The "Effective Date"               450,000

          For all purposes of this Agreement, the "Effective Date" shall be the
     date as of which Optionee no longer serves as President and Chief Executive
     Officer under the terms of that certain Supplemental Agreement dated
     November 17, 1998 between Optionee and the Company."

3.   Item 5E of the Agreement is hereby amended to read as follows:

               "E.  Exercise of Options by Optionee. The Option shall be 
                    -------------------------------     
     exercisable only to the extent exercisable as set forth in Paragraph A
     above and must be exercised on or before the date that is five (5) years
     following the Effective Date. To the extent any portion of the Option is
     not exercised within the time period provided, such portion of the Option
     shall terminate as of the date of expiration of such time period. Nothing
     in the Plan shall be construed as imposing any obligation on the Company to
     continue the employment of Optionee or shall interfere or restrict in any
     way the rights of the Company to discharge Optionee at any time for any
     reason whatsoever, with or without cause."
                                      
                                       6


<PAGE>
 
4.   Item 5F of the Agreement is hereby amended to read as follows:

               "F.  Exercise of Options After Death of Optionee. In the event of
                    -------------------------------------------
     the death of the Optionee, the personal representative of the Optionee may,
     subject to the provisions hereof and before the earlier of the Option's
     expiration date as set forth in Paragraph E above or the expiration of one
     (1) year after the date of such death, exercise the Option granted to the
     Optionee to the same extent the Optionee might have exercised such Option
     on the date of his death, but not further or otherwise. To the extent any
     portion of the Option is not exercised within the time period provided,
     such portion of the Option shall terminate as of the date of expiration of
     such time period."

     IN WITNESS WHEREOF, this Agreement has been duly executed as of the 17th 
day of November, 1998.

OPTIONEE:                               AIRTRAN HOLDINGS, INC.

                         (SEAL)         By: /s/ Robert D. Swenson 
_________________________                   -------------------------
D. JOSEPH CORR                                  Robert D. Swenson
                                        Title:  Chairman of the Board 

                                       7
<PAGE>
 
                                                                     EXHIBIT "B"
                                 AMENDMENT TO
                            STOCK OPTION AGREEMENT

     THIS IS AN AMENDMENT (the "Amendment") to that certain Stock Option
Agreement dated November 25, 1997 (the "Agreement") between AIRTRAN HOLDINGS,
INC., a Nevada corporation (the"Company") and D. JOSEPH CORR (the" Optionee").
Under the Agreement, Optionee was granted options to purchase 150,000 shares at
$5.50 per share.

     In consideration of Optionee's past and future employment with the Company 
and its subsidiaries and other good and valuable consideration, the receipt and
sufficency of which are hereby acknowledged, the parties acknowledge and agree 
as follows:

1.   Item 2B of the Agreement is hereby amended to read as follows:

             "B.    Options granted under this Agreement shall constitute
     nonqualified stock options."  


2.   The vesting schedule contained in Item 5A of the Agreement is hereby 
     amended to read as follows:

                              "Vesting Schedule
                               ----------------    

                    As of                 Number of Option Shares Exercisable
                    -----                 -----------------------------------

                    November 17, 1998                  50,000
                    The "Effective Date"              100,000

     Optionee will have the vested right to exercise the remaining 50,000
options only if the Effective Date occurs on or after November 17, 1999
(which is not anticipated). If the Effective Date occurs prior to November 17,
1999, then the option to purchase the remaining 50,000 shares shall lapse as
of the Effective Date.

     For all purposes of this Agreement, the "Effective Date" shall be the date
as of which Optionee no longer serves as President and Chief Executive Officer
under the terms of that certain Supplemental Agreement dated November 17, 1998
between Optionee and the Company".

3.   Item 5E of the Agreement is hereby amended to read as follows:

             "E.    Exercise of Options by Optionee. The Option shall be 
                    -------------------------------
exercisable only to the extent exercisable as set forth in Paragraph A above
and must be exercised on or before the date that is five (5) years following
the Effective Date. To the extent any portion of the Option is not exercised
within the time period provided, such portion of the Option shall terminate as
of the date of expiration of such time period. Nothing in the Plan shall be     
                    
                                       8
<PAGE>
 
     construed as imposing any obligation on the Company to continue the
     employment of Optionee or shall interfere or restrict in any way the rights
     of the Company to discharge Optionee at any time for any reason whatsoever,
     with or without cause."

4.   Item 5F of the Agreement is hereby amended to read as follows:

               "F.  Exercise of Options After Death of Optionee.  In the event 
                    --------------------------------------------
     of the death of the Optionee, the personal representative of the Optionee
     may, subject to the provisions hereof and before the earlier of the
     Option's expiration date as set forth in Paragraph E above or the
     expiration of one (1) year after the date of such death, exercise the
     Option granted to the Optionee to the same extent the Optionee might have
     exercised such Option on the date of his death, but not further or
     otherwise. To the extent any portion of the Option is not exercised within
     the time period provided, such portion of the Option shall terminate as of
     the date of expiration of such time period."

     IN WITNESS WHEREOF, this Agreement has been duly executed as of the 17th
day of November, 1998.

OPTIONEE:                              AIRTRAN HOLDINGS, INC.

/s/ D. Joseph Corr(SEAL)               By: /s/ Robert D. Swenson
------------------                        -------------------------
D. JOSEPH CORR                                 Robert D. Swenson
                                       Title:  Chairman of the Board 

                                       9