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                                                                    EXHIBIT 4.1

                    [TOREADOR ROYALTY CORPORATION LETTERHEAD]


March 15, 1999



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RE:  Series A Convertible Preferred Stock

Gentlemen:

Reference is made to that certain Securities Purchase Agreement (the "SPA"),
dated as of December 16, 1998, by and between Toreador Royalty Corporation (the
"Corporation"), and each of the persons listed on the Schedule of Purchasers
attached hereto (the "Purchasers") and the Certificate of Designation of Series
A Convertible Preferred Stock of Toreador Royalty Corporation (the "COD").
Capitalized terms used herein that are not specifically defined shall have the
meanings assigned to them in the SPA or the COD.

For good and valuable consideration, the receipt and sufficiency of which are
hereby acknowledged, it is understood and agreed as follows:

         1. Cash Dividends Only. The Corporation shall not exercise its option
under Paragraph 2 of the COD to pay dividends in additional shares of Preferred
Stock and shall instead pay all dividends in cash.

         2. Delayed Optional Redemption. The Corporation shall not exercise its
right of redemption under Paragraph 6 of the COD prior to December 1, 2004. In
the event of an Optional Redemption on or after December 1, 2004, the Optional
Redemption Price to be paid to a Holder shall be (notwithstanding Paragraph 6(b)
of the COD) the Liquidation Preference of the Preferred Shares then held by such
a Holder multiplied by (i) 1.03 if the Optional Redemption Date is on or after
December 1, 2004 but before December 1, 2005, (ii) 1.02 if the Optional
Redemption Date is on or after December 1, 2005 but before December 1, 2006,
(iii) 1.01 if the Optional Redemption Date is on or after December 1, 2006 and
before December 1, 2007, or (iv) 1.00 if the Optional Redemption Date is on or
after December 1, 2007, plus in all cases, accrued and unpaid dividends through
and including the Optional Redemption Date.



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March 15, 1999
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         3. No Mandatory Redemption. The Mandatory Redemption under Paragraph 7
of the COD shall not be recognized by either the Corporation or the Purchasers.
Instead, the Preferred Stock shall continue to accrue and pay dividends and
remain in full force and effect as otherwise provided by the COD.

         4. Successors and Assigns. The terms and conditions of this side letter
agreement (the "Agreement") shall inure to the benefit of and be binding upon
the respective successors and permitted assigns of the parties. Nothing in this
Agreement, express or implied, is intended to confer upon any party other than
the parties hereto or their respective successors and permitted assigns any
rights, remedies, obligations or liabilities under or by reason of this
Agreement, except as expressly provided in this Agreement. The Purchaser may
assign its rights and obligations hereunder, in connection with any private sale
or transfer of the Preferred Shares in accordance with the terms hereof, as long
as, as a condition precedent to such transfer, the transferee executes an
acknowledgment agreeing to be bound by the applicable provisions of this
Agreement, in which case the term "Purchaser" shall be deemed to refer to such
transferee as though such transferee were an original signatory hereto. The
Corporation may not assign it rights or obligations under this Agreement.

         5. Independent Nature of Purchasers' Obligations and Rights. The
obligations of each Purchaser hereunder are several and not joint with the
obligations of the other Purchasers hereunder, and no Purchaser shall be
responsible in any way for the performance of the obligations of any other
Purchaser hereunder. Nothing contained herein or in any other agreement or
document delivered herewith, and no action taken by any Purchaser pursuant
hereto or thereto, shall be deemed to constitute the Purchasers as a
partnership, an association, a joint venture or any other kind of entity, or
create a presumption that the Purchasers are in any way acting in concert with
respect to such obligations or the transactions contemplated by this Agreement.
Each Purchaser shall be entitled to protect and enforce its rights, including
without limitation the rights arising out of the Certificate of Designation,
this Agreement or the other Transaction Documents, and it shall not be necessary
for any other Purchaser to be joined as an additional party in any proceeding
for such purpose.

         6. Headings. The headings used in this Agreement are used for
convenience only and are not to be considered in construing or interpreting this
Agreement.





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         Please sign and date this letter in the space provided below to confirm
your agreement to the terms hereof.


                                        Very truly yours,


                                        TOREADOR ROYALTY CORPORATION



                                        By:      /S/ G. THOMAS GRAVES III  
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                                                 G. Thomas Graves III
                                                 Chief Executive Officer



Accepted and Agreed to by:


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By:
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       [Name]