<PAGE>   1
                                                                   EXHIBIT 4.1.2


                        CERTIFICATE OF SECOND AMENDMENT
                                       TO
                       CERTIFICATE OF LIMITED PARTNERSHIP
                                       OF
                      MEWBOURNE ENERGY PARTNERS 96-A, L.P.

         The Certificate of Second Amendment to Certificate of Limited
Partnership of MEWBOURNE ENERGY PARTNERS 96-A, L.P. (the "Partnership") is
being executed and filed by the undersigned general partners under the Delaware
Revised Uniform Limited Partnership Act.

                                  ARTICLE ONE

                 In order to reflect the assignment and withdrawal by certain
         general partners of their General Partner Interest in the Partnership
         and the substitution of their respective transferees as a substituted
         General Partner in the Partnership, Exhibit A to the Certificate of
         Limited Partnership of the Partnership, as previously amended by that
         certain Certificate of Amendment to Certificate of Limited Partnership
         dated November 7, 1996, is hereby deleted and such Exhibit A is hereby
         restated as set forth in Exhibit A hereto.


                                  ARTICLE TWO

         Article Four of the Certificate of Limited Partnership of the
Partnership is hereby amended in its entirety to read as follows:

                 The name and business address of the managing general partner
         of the Partnership is Mewbourne Development Corporation, 3901 S.
         Broadway, Tyler, Texas 75701.  The names of the investor general
         partners admitted to the Partnership are set forth on Exhibit A
         hereto.  The business address of the investor general partners is 3901
         S. Broady, Tyler, Texas 75701.

         IN WITNESS WHEREOF, the undersigned, the Managing Partner by and
through a duly authorized officer thereof acting for itself and as
attorney-in-fact for each of the General Partners set forth on Exhibit A has
executed this Certificate of Amendment to Certificate of Limited Partnership on
this 12th day of December, 1996.

                                    MEWBOURNE DEVELOPMENT CORPORATION,
                                    acting for itself and as attorney-in-fact
                                    for each of the General Partners as set
                                    forth on Exhibit A



                                    By:     /s/ J. Roe Buckley
                                       ---------------------------------
                                            J. Roe Buckley, Treasurer
<PAGE>   2


EXHIBIT A
GENERAL PARTNER INTEREST

MEWBOURNE ENERGY PARTNERS 96-A


<TABLE>
<CAPTION>
General Partner Interest                   State of Residence
------------------------                   ------------------
<S>                                                <C>
Priscilla J. Bair                                  PA

Leslie L. Bear                                     PA

Dale W. & Lillian R. Beebee                        NY

James G. & Wanda F. Bennett                        MO

William C. Bickel                                  PA

Doris M. Bishop                                    VA

Blackman Family Trust
James & Virginia Blackman                          AZ

Anne M. Blackwood Trust
Anne M. Blackwood, Trustee                         TX

Frederick W. Bode                                  PA

Mark J. Bowman                                     IL

William L. & Nancy H. Brach                        NJ

Barry H. Bredt                                     PA

William Joseph Brinn, Jr                           ND

James C. Britt                                     MD

Brook Family Trust
Arthur H. & Mary P. Brook, Trustees                CA

Esther L. Bucher                                   DE
</TABLE>
<PAGE>   3
<TABLE>
<S>                                                <C>
Esther Calcaterra Revocable Living Trust
Esther Calcaterra, Trustee                         MO

Luz M. & Jose M. Cantellops, M.D.                  PA

L. Robert Castorr                                  MD

Alvin E. & Shirley A. Catlett                      OH

Phillip W. Chao                                    DE

Linda S. Cohen                                     VA

Conrad Family Trust Dated 8/28/95
William D. & Eloise D. Conrad, Trustees            AZ

D. N. Coupard Rev. Trust
P. E. Coupard Rev. Trust
D. N. & P. E. Coupard, Trustees                    MD

Clare Crawford-Mason                               DC

Herbert L. & M. Arlene Culp                        PA

R. Russell Darby                                   PA

Paul R. Davis                                      UT

Del-Kijaico, Inc.                                  DE

Paul I. Detwiler, Jr.
Patricia B. Detwiler                               PA

Timothy R. & Nandy L. Dorlac                       MO

Donald J. Dorr                                     MO

William A. Dougherty                               VA

Mary Lou Doyle                                     MD

Willard B. & Evelyn P. Dunn                        PA

The Engle Trust
Charles V. & Marjorie C. Engle                     CA
</TABLE>
<PAGE>   4
<TABLE>
<S>                                                <C>
Maximo Fernandez Leeds Trust
Max F. Leeds, Trustee                              CA

George Figacz Trust
George Figacz, Trustee                             MI

Mary Flauaus Revocable Living Trust
Mary M. Wurtz, Trustee                             MO

Alice Virginia D. Fletcher                         MD

John & Betty Foor                                  NY

Francus Family Ltd. Partnership
Cyril Francus General Partner                      NJ

Stephen J. Fukayama                                IL

John J. Getz Sr. Revocable Trust
Ann I. Getz Revocable Trust
John J. & Ann I. Getz, Trustees                    NJ

Edward Gilbert                                     MD

Dorothy I. Goggio                                  MO

Morton Goldfield                                   PA

Vivian F. Goode                                    MD

Gary E. Gottfredson                                UT

Richard J. & Mary M. Grich                         VA

Helen F. Grim                                      PA

David L. & Diane M. Grubbs                         MO

Joan M. Gruebner Living Trust
Herman W. Gruebner, Trustee                        IL

John E. Gusto Trust
John E. Gusto, Trustee                             CA

George E. & Judith L. Guttschalk                   TX
</TABLE>
<PAGE>   5
<TABLE>
<S>                                                <C>
Don E. & Gloria F. Hamrick                         VA

Deborah A. & James E. Hanshall                     CA

Timothy A. Harrison                                NC

Allan L. Higgins                                   IL

Peter F. Hille                                     CA

Floyd & Alice Ho                                   DE

LaRue A. & Any M. Hoffman Family Trust             CA

Patricia N. Holland                                MD

Donald K. & Cathline S. Ingram                     MD

C. Russell & Anita D. Johnson                      PA

Johnson Loving Trust
Susan G. Johnson, Trustee                          TX

Lloyd E. Kaiser                                    PA

Jasmat N. Kansagra, M.D. &
Niramala J. Kansagra                               PA

Robert B. & Bernice F. Kay                         PA

Kehres Family Trust
Jesse W. & Ester A. Kehres, Trustees               CA

David K. Kennedy                                   DE

Kerr Family Trust Dated 7/20/89
Robert A. & Janet F. Kerr, Trustees                CA

Rosemary Kinder Revocable Living Trust
Rosemary Kinder, Trustee                           MO

Kenneth W. & Donna M. Klatch                       MO

John J. Klocko                                     DE
</TABLE>
<PAGE>   6
<TABLE>
<S>                                                <C>
Thomas Michael & Anne L. Knasel                    OH

Wiliam L. Kraus, III                               DE

Dennis L. Krause                                   DE

Lawrence G. Lareau                                 PA

Paul G. Lehmitz                                    UT

Edward G. Lippitt                                  WV

Gilbert W. & Lula G. Lord                          VA

Rose Lorie Trust
Richard A. Bishop, Trustee                         DC

Andrew & Barbara Magiera                           MI

Patricia Jean Manzo Trust                          CA

Robert S. Marcus                                   PA

Gordon R. Masters                                  MD

Robert E. & Mary F. McGlaughlin                    MO

John G. Mergner, Sr.                               MD

Ralph W. Minard Living Trust
Ralph W. Minard, Trustee                           IL

Richard C. Minto Trust
Richard C. Minto, Trustee                          MO

C. W. Moore                                        WV

Alexander S. Morrison                              SC

Robert E. Mortensen                                PA

Nancy G. Nation                                    TX

John C. & Mildred Estes New                        MD
</TABLE>
<PAGE>   7
<TABLE>
<S>                                                <C>
Lloyd C. Newsom                                    NJ

Ronald D. Nielsen                                  UT

Gary A. & Kathleen E. Novotny                      CA

Timothy I. & Helen C. O'Hearn                      TX

Robert E. O'Neill                                  IL

Claudia H. Peters                                  PA

Nancy L. Petrovich                                 PA

Gregory T. & Carol A. Rada                         PA

Radhica Ramrattan                                  MD

Marian M. Reagan                                   TN

Thomas E. & Mary Anne Rebernak                     IL


Ben E. Rodell Revocable Living Trust
Ben E. Rodell, Trustee                             MO

Gordon & Deborah H. Schirm                         OH

Maurice Schneider                                  DE

David R. Schroeder Living Trust
David R. & Jan F. Schroeder, Trustees              IL

Stuart L. Schwotzer                                OH

Tina R. Sigman Living Trust
Tina R. Sigman, Trustee                            MO

Vernon P. & Lida S. Simmons                        VA

Paul A. Skaff                                      WV

Fred W. Sladek Trust
Fred W. Sladek, Trustee                            CA
</TABLE>
<PAGE>   8
<TABLE>
<S>                                                <C>
James C. Smith Jr. Rev. Trust
James C. Smith, Jr. Trustee                        VA

Josephine L. Smith                                 PA

Reynold B. Smith Trust B
Josephine L. Smith, Trustee                        PA

John J. Spillane                                   PA

Edward T. Sprock Trust
Edward T. Sprock, Trustee                          MI

Carol H. Straus                                    MD

Mary A. Suchan Revocable Living Trust              MO

Keith Sueker                                       PA

Gladyce T. Sumida                                  DC

Sarah H. Taylor                                    TN

George S. & Susan D. Temple                        MO

David H. Thomas                                    MO

Cary J. & Linda L. Thompson                        MO

Jack F. Traverso                                   DE

Mark J. & Deborah M. Troch                         MD

Ka Khy & Sayeda Tze                                DE

Valetta                                            PA

Barbara Waldman                                    MD

Wamhoff Revocable Trust
Robert E. & Diane F. Wamhoff, Trustees             MO

Russell F. & Laurie A. Warren                      CT

Estate of Carl Weiland
</TABLE>
<PAGE>   9
<TABLE>
<S>                                                <C>
Barbara Waldman, Personal Rep.                     MD

Ira Wharton                                        WV

B. E. Williams                                     WV

Timothy & Janet Wills                              CA

Stanley A. Witzel                                  NJ

Richard & Kathleen Wolter                          NJ

Dennis P. Yarnell                                  DE

Barnet D. & Jane R. Zeldin                         PA
</TABLE>
<PAGE>   10
EXHIBIT B
LIMITED PARTNER INTEREST

MEWBOURNE ENERGY PARTNERS 96-A

<TABLE>
<CAPTION>
Limited Partner Interest                   State of Residence
------------------------                   ------------------
<S>                                                <C>
Bruce Addison                                      FL

Francus Family Ltd. Partnership
Cyril Francus General Partner                      NJ

Helen F. Grim                                      PA

Timothy A. Harrison                                NC

Johnson Loving Trust
Susan G. Johnson, Trustee                          TX

Thomas Michael & Anne L. Knasel                    OH

Patricia Jean Manzo Trust                          CA

Andy Lee McCollum                                  IL

Robert E. O'Neill                                  IL

Marian M. Reagan                                   TN

John E. Sayler                                     PA

Josephine L. Smith                                 PA

Reynold B. Smith Trust B
Josephine L. Smith, Trustee                        PA

Sarah H. Taylor                                    TN

Russell F. & Laurie A. Warren                      CT

Stanley A. Witzel                                  NJ
</TABLE>