SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                 Schedule 13D**

                    Under the Securities Exchange Act of 1934
                               (Amendment No. 31)*

                          San Juan Basin Royalty Trust
                                (Name of Issuer)

                          Units of Beneficial Interest
                         (Title of Class of Securities)

                                    798241105
                                 (Cusip Number)

                               J. Taylor Crandall
                           201 Main Street, Suite 3100
                             Fort Worth, Texas 76102
                              (817) 390-8400 (Name,
                         Address and Telephone Number of
                                     Person
                Authorized to Receive Notices and Communications)

                                  May 19, 2003
             (Date of Event which Requires Filing of this Statement)

If the filing person has previously filed a statement on Schedule 13G to report
the acquisition which is the subject of this Schedule 13D, and is filing this
schedule because of Rule 13d-1(e), 13d-1(f) or 13d-1(g), check the following box
[_].

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).

**The total number of Depositary Units reported herein is 10,241,100, which
constitutes approximately 22.0% of the total number of Units of Beneficial
Interest outstanding. All ownership percentages set forth herein assume that
there are 46,608,796 Units of Beneficial Interest outstanding.



--------------------------------------------------------------------------------
1.       Name of Reporting Person:

                  Alpine Capital, L.P.
--------------------------------------------------------------------------------
2.       Check the Appropriate Box if a Member of a Group:
                                                        (a)     [_]
                                                        (b)     [X]
--------------------------------------------------------------------------------
3.       SEC Use Only


--------------------------------------------------------------------------------
4.       Source of Funds: WC


--------------------------------------------------------------------------------
5.       Check box if Disclosure of Legal Proceedings is Required Pursuant to
         Items 2(d) or 2(e):
                                                                [_]
--------------------------------------------------------------------------------
6.       Citizenship or Place of Organization: Texas


--------------------------------------------------------------------------------
                                7.      Sole Voting Power: 9,477,200 (1)
Number of
Units                           ------------------------------------------------
Beneficially                    8.      Shared Voting Power: -0-
Owned By
Each                            ------------------------------------------------
Reporting                       9.      Sole Dispositive Power: 9,477,200 (1)
Person
With                            ------------------------------------------------
                                10.     Shared Dispositive Power: -0-

--------------------------------------------------------------------------------
11.      Aggregate Amount Beneficially Owned by Each Reporting Person:

                  9,477,200
--------------------------------------------------------------------------------
12.      Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                                        [_]
--------------------------------------------------------------------------------
13.      Percent of Class Represented by Amount in Row (11): 20.3%


--------------------------------------------------------------------------------
14.      Type of Reporting Person: PN


--------------------------------------------------------------------------------
------------------------
(1)  Power is exercised through its two general partners, Robert W. Bruce III
     and Algenpar, Inc.



--------------------------------------------------------------------------------
1.       Name of Reporting Person:

                  Robert W. Bruce III
--------------------------------------------------------------------------------
2.       Check the Appropriate Box if a Member of a Group:
                                                        (a)     [_]
                                                        (b)     [X]
--------------------------------------------------------------------------------
3.       SEC Use Only


--------------------------------------------------------------------------------
4.       Source of Funds: Not Applicable


--------------------------------------------------------------------------------
5.       Check box if Disclosure of Legal Proceedings is Required Pursuant to
         Items 2(d) or 2(e):
                                                                [_]
--------------------------------------------------------------------------------
6.       Citizenship or Place of Organization: USA


--------------------------------------------------------------------------------
                                7.      Sole Voting Power: -0-
Number of
Units                           ------------------------------------------------
Beneficially                    8.      Shared Voting Power: 9,477,200 (1)
Owned By
Each                            ------------------------------------------------
Reporting                       9.      Sole Dispositive Power: -0-
Person
With                            ------------------------------------------------
                                10.     Shared Dispositive Power: 9,477,200 (1)

--------------------------------------------------------------------------------
11.      Aggregate Amount Beneficially Owned by Each Reporting Person:

                  9,477,200 (1)
--------------------------------------------------------------------------------
12.      Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                                        [_]
--------------------------------------------------------------------------------
13.      Percent of Class Represented by Amount in Row (11): 20.3%


--------------------------------------------------------------------------------
14.      Type of Reporting Person: IN


--------------------------------------------------------------------------------
------------------------
(1)  Solely in his capacity as one of two general partners of Alpine Capital,
     L.P.



--------------------------------------------------------------------------------
1.       Name of Reporting Person:

                  Algenpar, Inc.
--------------------------------------------------------------------------------
2.       Check the Appropriate Box if a Member of a Group:
                                                        (a)     [_]
                                                        (b)     [X]
--------------------------------------------------------------------------------
3.       SEC Use Only


--------------------------------------------------------------------------------
4.       Source of Funds: Not Applicable


--------------------------------------------------------------------------------
5.       Check box if Disclosure of Legal Proceedings is Required Pursuant to
         Items 2(d) or 2(e):
                                                                [_]
--------------------------------------------------------------------------------
6.       Citizenship or Place of Organization: Texas


--------------------------------------------------------------------------------
                                7.      Sole Voting Power: -0-
Number of
Units                           ------------------------------------------------
Beneficially                    8.      Shared Voting Power: 9,477,200 (1)(2)
Owned By
Each                            ------------------------------------------------
Reporting                       9.      Sole Dispositive Power: -0-
Person
With                            ------------------------------------------------
                                10.     Shared Dispositive Power: 9,477,200 (1)
                                                                            (2)
--------------------------------------------------------------------------------
11.      Aggregate Amount Beneficially Owned by Each Reporting Person:

                  9,477,200 (2)
--------------------------------------------------------------------------------
12.      Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                                        [_]
--------------------------------------------------------------------------------
13.      Percent of Class Represented by Amount in Row (11): 20.3%


--------------------------------------------------------------------------------
14.      Type of Reporting Person: CO


--------------------------------------------------------------------------------
------------------------
(1)  Power is exercised through its President, J. Taylor Crandall.
(2)  Solely in its capacity as one of two general partners of Alpine Capital,
     L.P.



--------------------------------------------------------------------------------
1.       Name of Reporting Person:

                  J. Taylor Crandall
--------------------------------------------------------------------------------
2.       Check the Appropriate Box if a Member of a Group:
                                                        (a)     [_]
                                                        (b)     [X]
--------------------------------------------------------------------------------
3.       SEC Use Only


--------------------------------------------------------------------------------
4.       Source of Funds: Not Applicable


--------------------------------------------------------------------------------
5.       Check box if Disclosure of Legal Proceedings is Required Pursuant to
         Items 2(d) or 2(e):
                                                                [_]
--------------------------------------------------------------------------------
6.       Citizenship or Place of Organization: USA


--------------------------------------------------------------------------------
                                7.      Sole Voting Power: -0-
Number of
Units                           ------------------------------------------------
Beneficially                    8.      Shared Voting Power: 9,477,200 (1)
Owned By
Each                            ------------------------------------------------
Reporting                       9.      Sole Dispositive Power: -0-
Person
With                            ------------------------------------------------
                                10.     Shared Dispositive Power: 9,477,200 (1)

--------------------------------------------------------------------------------
11.      Aggregate Amount Beneficially Owned by Each Reporting Person:

                  9,477,200 (1)
--------------------------------------------------------------------------------
12.      Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                                        [_]
--------------------------------------------------------------------------------
13.      Percent of Class Represented by Amount in Row (11): 20.3%


--------------------------------------------------------------------------------
14.      Type of Reporting Person: IN


--------------------------------------------------------------------------------
------------------------
(1)  Solely in his capacity as President and sole stockholder of Algenpar, Inc.,
     which is one of two general partners of Alpine Capital, L.P.



--------------------------------------------------------------------------------
1.       Name of Reporting Person:

                  Keystone, Inc.
--------------------------------------------------------------------------------
2.       Check the Appropriate Box if a Member of a Group:
                                                        (a)     [_]
                                                        (b)     [X]
--------------------------------------------------------------------------------
3.       SEC Use Only


--------------------------------------------------------------------------------
4.       Source of Funds: WC


--------------------------------------------------------------------------------
5.       Check box if Disclosure of Legal Proceedings is Required Pursuant to
         Items 2(d) or 2(e):
                                                                [_]
--------------------------------------------------------------------------------
6.       Citizenship or Place of Organization: Texas


--------------------------------------------------------------------------------
                                7.      Sole Voting Power: 763,900 (1)
Number of
Units                           ------------------------------------------------
Beneficially                    8.      Shared Voting Power: -0-
Owned By
Each                            ------------------------------------------------
Reporting                       9.      Sole Dispositive Power: 763,900 (1)
Person
With                            ------------------------------------------------
                                10.     Shared Dispositive Power: -0-

--------------------------------------------------------------------------------
11.      Aggregate Amount Beneficially Owned by Each Reporting Person:

                  763,900
--------------------------------------------------------------------------------
12.      Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                                        [_]
--------------------------------------------------------------------------------
13.      Percent of Class Represented by Amount in Row (11): 1.6%


--------------------------------------------------------------------------------
14.      Type of Reporting Person: CO


--------------------------------------------------------------------------------
------------------------
(1)  Power is exercised through its President, Robert M. Bass.



--------------------------------------------------------------------------------
1.       Name of Reporting Person:

                  Robert M. Bass
--------------------------------------------------------------------------------
2.       Check the Appropriate Box if a Member of a Group:
                                                        (a)     [_]
                                                        (b)     [X]
--------------------------------------------------------------------------------
3.       SEC Use Only


--------------------------------------------------------------------------------
4.       Source of Funds: Not Applicable


--------------------------------------------------------------------------------
5.       Check box if Disclosure of Legal Proceedings is Required Pursuant to
         Items 2(d) or 2(e):
                                                                [_]
--------------------------------------------------------------------------------
6.       Citizenship or Place of Organization: USA


--------------------------------------------------------------------------------
                                7.      Sole Voting Power: 763,900 (1)
Number of
Units                           ------------------------------------------------
Beneficially                    8.      Shared Voting Power: -0-
Owned By
Each                            ------------------------------------------------
Reporting                       9.      Sole Dispositive Power: 763,900 (1)
Person
With                            ------------------------------------------------
                                10.     Shared Dispositive Power: -0-

--------------------------------------------------------------------------------
11.      Aggregate Amount Beneficially Owned by Each Reporting Person:

                  763,900 (1)
--------------------------------------------------------------------------------
12.      Check Box if the Aggregate Amount in Row (11) Excludes Certain Units:

                                                                        [_]
--------------------------------------------------------------------------------
13.      Percent of Class Represented by Amount in Row (11): 1.6%


--------------------------------------------------------------------------------
14.      Type of Reporting Person: IN


--------------------------------------------------------------------------------
------------------------
(1)  Solely in his capacity as President of Keystone, Inc.



Pursuant to Regulation 13D-G of the General Rules and Regulations under the
Securities Exchange Act of 1934, as amended (the "Act"), the undersigned hereby
amend their Schedule 13D Statement dated April 1, 1999, as amended by Amendment
No. 1 dated April 13, 1999, as amended by Amendment No. 2 dated May 18, 1999, as
amended by Amendment No. 3 dated May 25, 1999, as amended by Amendment No. 4
dated June 29, 1999, as amended by Amendment No. 5 dated August 4, 1999, as
amended by Amendment No. 6 dated August 20, 1999, as amended by Amendment No. 7
dated September 8, 1999, as amended by Amendment No. 8 dated September 27, 1999,
as amended by Amendment No. 9 dated October 13, 1999, as amended by Amendment
No. 10 dated October 25, 1999, as amended by Amendment No. 11 dated November 5,
1999, as amended by Amendment No. 12 dated November 29, 1999, as amended by
Amendment No. 13 dated December 9, 1999, as amended by Amendment No. 14 dated
December 20, 1999, as amended by Amendment No. 15 dated January 13, 2000, as
amended by Amendment No. 16 dated January 26, 2000, as amended by Amendment No.
17 dated February 17, 2000, as amended by Amendment No. 18 dated March 17, 2000,
as amended by Amendment No. 19 dated April 17, 2000, as amended by Amendment No.
20 dated April 18, 2001, as amended by Amendment No. 21 dated April 30, 2001, as
amended by Amendment No. 22 dated May 17, 2001, as amended by Amendment No. 23
dated September 19, 2001, as amended by Amendment No. 24 dated March 19, 2002,
as amended by Amendment No. 25 dated July 1, 2002, as amended by Amendment No.
26 dated July 9, 2002, as amended by Amendment No. 27 dated February 6, 2003, as
amended by Amendment No. 28 dated February 28, 2003, as amended by Amendment No.
29 dated March 6, 2003, as amended by Amendment No. 30 dated April 23, 2003 (the
"Schedule 13D"), relating to the Units of Beneficial Interest (the "Units"), of
San Juan Basin Royalty Trust (the "Issuer"). Unless otherwise indicated, all
defined terms used herein shall have the same meanings respectively ascribed to
them in the Schedule 13D.

Item 1. SECURITY AND ISSUER.

No material change.

Item 2. IDENTITY AND BACKGROUND.

No material change.

Item 3. SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.

Item 3 is hereby amended and restated in its entirety as follows:

The source and amount of the funds used by the Reporting Persons to purchase
Units are as follows:


REPORTING PERSON               SOURCE OF FUNDS              AMOUNT OF FUNDS
----------------               ---------------              ---------------

Alpine                         Working Capital(1)           $125,049,714.07 (2)

R. Bruce                       Not Applicable               Not Applicable



REPORTING PERSON               SOURCE OF FUNDS              AMOUNT OF FUNDS
----------------               ---------------              ---------------

Algenpar                       Not Applicable               Not Applicable

Crandall                       Not Applicable               Not Applicable

Keystone                       Working Capital(1)           $ 7,506,643.15

R. Bass                        Not Applicable               Not Applicable

(1) As used herein, the term "Working Capital" includes income from the business
operations of the entity plus sums borrowed from banks and brokerage firm margin
accounts to operate such business in general. None of the funds reported herein
as "Working Capital" were borrowed or otherwise obtained for the specific
purpose of acquiring, handling, trading or voting the Units.

(2) This figure represents the total amount expended by Alpine for all purchases
of the Stock without subtracting sales; therefore, such figure does not
represent Alpine's net investment in the Stock. Alpine's net investment in the
Stock is $33,352,741.30.

Item 4. PURPOSE OF TRANSACTION.

No material change.

Item 5. INTEREST IN SECURITIES OF THE ISSUER.

Item 5 has been amended and restated in its entirety as follows:

(a)

ALPINE

The aggregate number of Units that Alpine owns beneficially, pursuant to Rule
13d-3(d)(1)(i) of the Act, is 9,477,200, which constitutes approximately 20.3%
of the outstanding Units.

R. BRUCE

Because of his position as one of two general partners of Alpine, R. Bruce may,
pursuant to Rule 13d-3 of the Act, be deemed to be the beneficial owner of
9,477,200 Units, which constitutes approximately 20.3% of the outstanding Units.

ALGENPAR

Because of its position as one of two general partners of Alpine, Algenpar may,
pursuant to Rule 13d-3 of the Act, be deemed to be the beneficial owner of
9,477,200 Units, which constitutes approximately 20.3% of the outstanding Units.

CRANDALL



Because of his position as President and sole stockholder of Algenpar, one of
two general partners of Alpine, Crandall may, pursuant to Rule 13d-3 of the Act,
be deemed to be the beneficial owner of 9,477,200 Units, which constitutes
approximately 20.3% of the outstanding Units.

KEYSTONE

The aggregate number of Units that Keystone owns beneficially, pursuant to Rule
13d-3(d)(1)(i) of the Act, is 763,900, which constitutes approximately 1.6% of
the outstanding Units.

R. BASS

Because of his position as President of Keystone, R. Bass may, pursuant to Rule
13d-3 of the Act, be deemed to be the beneficial owner of 763,900 Units, which
constitutes approximately 1.6% of the outstanding Units.

To the best of the knowledge of each of the Reporting Persons, other than as set
forth above, none of the persons named in Item 2 herein is the beneficial owner
of any Units.

(b)

ALPINE

Acting through its two general partners, Alpine has the sole power to vote or to
direct the vote and to dispose or to direct the disposition of 9,477,200 Units.

R. BRUCE

As one of two general partners of Alpine, R. Bruce has shared power to vote or
to direct the vote and to dispose or to direct the disposition of 9,477,200
Units.

ALGENPAR

As one of two general partners of Alpine, Algenpar has shared power to vote or
to direct the vote and to dispose or to direct the disposition of 9,477,200
Units.

CRANDALL

As the President and sole stockholder of Algenpar, which is one of two general
partners of Alpine, Crandall has shared power to vote or to direct the vote and
to dispose or to direct the disposition of 9,477,200 Units.

KEYSTONE

Acting through its President, Keystone has the sole power to vote or to direct
the vote and to dispose or to direct the disposition of 763,900 Units.



R. BASS

As President of Keystone, R. Bass has sole power to vote or to direct the vote
and to dispose or to direct the disposition of 763,900 Units.

(c) Since the most recent filing on Schedule 13D, Alpine has sold Units in open
market transactions on the New York Stock Exchange as follows:

DATE                 NO. OF UNITS SOLD          PRICE PER UNIT
----                 -----------------          --------------

04/23/03                   20,700               $ 14.88
04/24/03                   34,100               $ 14.91
04/25/03                   24,800               $ 14.97
04/28/03                   13,000               $ 14.95
04/29/03                   37,000               $ 14.91
04/30/03                   43,000               $ 15.07
05/01/03                   24,400               $ 15.20
05/02/03                    32000               $ 15.32
05/05/03                   17,000               $ 15.31
05/06/03                   12,500               $ 15.36
05/07/03                    6,500               $ 15.34
05/08/03                    6,000               $ 15.35
05/09/03                    8,800               $ 15.31
05/12/03                   20,000               $ 15.35
05/13/03                   30,000               $ 15.47
05/14/03                   33,000               $ 15.73
05/15/03                   43,000               $ 15.99
05/16/03                   17,900               $ 15.95
05/19/03                  132,000               $ 16.19
05/20/03                   30,000               $ 16.35


Except as set forth in this paragraph (c), to the best of the knowledge of each
of the Reporting Persons, none of the persons named in response to paragraph (a)
has effected any transactions in the Units since the most recent filing on
Schedule 13D.

(d) Each of the Reporting Persons affirms that no person other than such
Reporting Person has the right to receive or the power to direct the receipt of
dividends from, or the proceeds from the sale of, the Units owned by such
Reporting Person.

(e) Not applicable.

Item 6. CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT TO
SECURITIES OF THE ISSUER.

No material change.

Item 7. MATERIAL TO BE FILED AS EXHIBITS.



Exhibit 99.1 -- Agreement pursuant to Rule 13d-1(k)(1)(iii), filed herewith.




         After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

DATED:  May 21, 2003

                                   ALPINE CAPITAL, L.P.

                                   By:  /s/ Robert W. Bruce III
                                        ---------------------------------------
                                        Robert W. Bruce III,
                                        Manager


                                   /s/ Robert W. Bruce III
                                   --------------------------------------------
                                   ROBERT W. BRUCE III


                                   ALGENPAR, INC.


                                   By:  /s/ J. Taylor Crandall
                                        ---------------------------------------
                                        J. Taylor Crandall,
                                        President


                                   /s/ J. Taylor Crandall
                                   --------------------------------------------
                                   J. TAYLOR CRANDALL


                                   KEYSTONE, INC.


                                   By:  /s/ Kevin G. Levy
                                        ---------------------------------------
                                        Kevin G. Levy,
                                        Vice President


                                   /s/ Kevin G. Levy
                                   --------------------------------------------
                                   KEVIN G. LEVY,

                                   Attorney-in-Fact for:

                                   ROBERT M. BASS (1)

------------------------
(1)  A Power of Attorney authorizing Kevin G. Levy, et al., to act on behalf of
Robert M. Bass previously has been filed with the Securities and Exchange
Commission.




                                  EXHIBIT INDEX


EXHIBIT           DESCRIPTION

99.1              Agreement pursuant to Rule 13d-1(k)(1)(iii), filed herewith.