<PAGE>   1
                                                                    EXHIBIT 4.13

                        LIMITED WAIVER OF COVENANTS UNDER
                    AND AMENDMENT TO SENIOR SUBORDINATED NOTE
                         AND WARRANT PURCHASE AGREEMENT


           This Limited Waiver of Covenants Under and Amendment to Senior
Subordinated Note and Warrant Purchase Agreement (this "Agreement") is dated as
of the 13th day of April, 2001, and is executed by and among Atlantic Premium
Brands, Ltd. ("Atlantic"), a Delaware corporation, Prefco Corp. ("Prefco"), a
Delaware corporation, Carlton Foods Corp. ("Carlton"), a Delaware corporation,
Richards Cajun Foods Corp. ("Richards"), a Delaware corporation, Grogan's Farm,
Inc. ("Grogan's"), a Delaware corporation, and Potter Sausage Co. ("Potter"), a
Delaware corporation (collectively, the "Sellers"), and Banc One Capital
Partners, LLC ("BOCP"), a Delaware limited liability company and Small Business
Investment Company (the "Purchaser").

                                    RECITALS:


           WHEREAS, the Sellers and the Purchaser executed the certain Senior
Subordinated Note and Warrant Purchase Agreement dated as of March 20, 1998 (the
"Purchase Agreement") and the certain Related Documents of even date therewith
(collectively, the "Purchase Documents") in connection with the issuance and
sale by Sellers to Purchaser of (i) the Senior Subordinated Note dated as of
March 20, 1998 in the aggregate principal amount of $6,500,000 (the "Note"),
(ii) the Warrant to purchase 666,947 shares of Nonvoting Common Stock of
Atlantic (the "Fixed Warrant"), and (iii) the Warrant to purchase up to 428,753
shares of Nonvoting Common Stock of Atlantic (the "Contingent Warrant", and
together with the Fixed Warrant, the "Warrants") (capitalized terms used but not
defined herein shall have the meanings ascribed in the Glossary of Defined Terms
attached as Exhibit A to the Purchase Agreement and incorporated therein); and

           WHEREAS, Section 9.1 of the Purchase Agreement requires the Company
to maintain a Fixed Charge Coverage Ratio of not less than 1.15 to 1.00 as of
the end of each Quarter (the "Section 9.1 Covenant"); and

           WHEREAS, Section 9.2 of the Purchase Agreement requires the Company
to maintain an Interest Coverage Ratio of not less than 1.75 to 1.00 as of the
end of each Quarter (the "Section 9.2 Covenant"); and
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           WHEREAS, Section 9.3 of the Purchase Agreement requires the Company
to maintain as of the end of each Quarter a ratio of Consolidated Indebtedness
outstanding as of the end of such Quarter to EBITDA for a period of four
consecutive Quarters ending as of the end of such Quarter of not greater than
5.00 to 1.00 (the "Section 9.3 Covenant"); and

           WHEREAS, Section 9.4 of the Purchase Agreement requires that, as of
the end of each Quarter, commencing with the Quarter ending September 30, 1998,
the consolidated stockholders' equity of the Company shall not be less than
$10,000,000 (the "Section 9.4 Covenant"); and

           WHEREAS, the Sellers have requested the Purchaser to waive the
Company's non-compliance with the Section 9.1 Covenant, the Section 9.2
Covenant, the Section 9.3 Covenant and the Section 9.4 Covenant (referred to
collectively as the "Section 9 Covenants") for certain periods hereinafter
specified;
and

           WHEREAS, the Purchaser is willing to waive the Company's
non-compliance with the Section 9 Covenants for the certain periods hereinafter
specified, and to make certain other limited waivers described herein, subject
to the terms and conditions hereof; and

           WHEREAS, the Purchaser and the Sellers desire to amend the Purchase
Documents as hereinafter provided, and to enter into the certain further
agreements set forth below.

                                   AGREEMENT:

           NOW, THEREFORE, in consideration of the mutual covenants contained
herein and intending to be legally bound hereby, the parties hereto agree as
follows:

           1. Limited Waiver of Covenants. The Purchaser hereby (a) waives the
Company's non-compliance with the Section 9 Covenants for the periods ending
June 30, 2000, September 30, 2000 and December 31, 2000, and (b) waives any
Event of Default associated therewith or occasioned thereby. The Purchaser
hereby also (a) waives the Company's performance under Section 6.1(a) of the
Purchase Agreement with respect to the Fiscal Year ended December 31, 2000 until
April 19, 2001, and permanently waives any notice pursuant to Section 6.6(b) of
the Purchase Agreement relating to the Company's non-performance under Section
6.1(a) of the Purchase Agreement with respect to the Fiscal Year ended December
31, 2000, and (b) waives any Event of Default associated therewith or occasioned
thereby. Further, the Purchaser hereby (a) waives the Company's compliance with
Section 8.10 of the Purchase Agreement with respect to (i) Sellers' entering
into the consulting agreement described in Section 4.3 hereof and (ii) the
transactions contemplated by the Sterling Agreement (as defined in Section 3
hereof), and (b) waives any Event of Default associated therewith or occasioned
thereby. Finally, the Purchaser hereby (a) waives any Event of Default under
Sections 8(c) and 8(f) of the Note associated with or occasioned by the
Company's failure to pay (i) the certain Seller note owing to Franklin Roth and
Allan Pauly due March 31, 2001, (ii) the certain Seller note owing to J. L.
Richard due July 31, 2001, and (iii) the certain Seller note owing to Bobby and
Betty Grogan due September 30, 2001, and (b) waives the Company's compliance
with the notice requirements under Sections 6.6(a) and 6.6(b) of the Purchase
Agreement with respect to any such Event of Default.

           2. Amendment of Purchase Documents. To induce the Purchaser to enter
into this Agreement, the Sellers agree that the Purchase Documents shall be and
are hereby amended as follows, which amendments shall supersede and prevail over
any conflicting provisions of the Purchase Documents:

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<PAGE>   3
           2.1       Amendment of Interest Provisions of Note. The Note is
                     amended to provide that, as of January 17, 2001, the Stated
                     Interest Rate shall be 15% per annum and the Default
                     Interest Rate shall be 18% per annum. At all times on and
                     after January 17, 2001 that the Default Rate is not in
                     effect, interest on the Note shall accrue at a rate equal
                     to the Stated Interest Rate, and shall be payable as
                     follows: (i) interest at the rate of 10% per annum shall be
                     paid monthly in arrears on each Payment Date specified in
                     the Note; and (ii) interest at the rate of 5% per annum
                     shall be compounded monthly and paid in full on June 30,
                     2003. After June 30, 2003, all accrued but unpaid interest
                     at the Stated Interest Rate shall be paid monthly in
                     arrears on each Payment Date specified in the Note.

           2.2        Amendment of Financial Covenants. Section 9 of the
                      Purchase Agreement is hereby deleted in its entirety and
                      is replaced with the provisions set forth in Exhibit "A"
                      attached hereto and made a part hereof, effective as of
                      January 1, 2001. BOCP acknowledges that from and after
                      January 1, 2001 it will not be entitled to assert any
                      breach of, or any Event of Default relating to, the
                      Section 9 Covenants as they existed prior to this
                      amendment thereof.

           2.3        Amendment to Notice Provision. Section 11.13(b) of the
                      Purchase Agreement is hereby amended to substitute the
                      following address as the current address of the Purchaser:

                                    Banc One Capital Partners, LLC
                                    191 West Nationwide Blvd.
                                    Suite 600
                                    Columbus, Ohio  43215
                                    Attention:  General Counsel
                                    Telephone No.  (614) 246-2440
                                    Fax No.  (614) 246-2441

           3. Sale of Note and Warrants to Sterling Advisors. The Sellers,
Purchaser and Sterling BOCP, LLC ("Sterling") have executed a certain Note and
Warrant Purchase Agreement of even date herewith (the "Sterling Agreement")
pursuant to which the Purchaser has agreed to sell to Sterling, and Sterling has
agreed to purchase from the Purchaser, ten percent (10%) of the Purchaser's
interest in the Purchase Agreement, the Note, the Warrants and certain related
rights and security agreements thereunder (the note to be held by Sterling as a
result of this transaction is referred to as the "Sterling Note" and the note to
be held by the Purchaser as a result of this transaction is referred to as the
"BOCP Note"). The Sellers agree that any default in performance of Sterling or
Sellers under the terms of the Sterling Agreement shall constitute a default in
performance under this Agreement.

           4.         Additional Covenants. Sellers and the Purchaser further
                      agree as follows:

           4.1       All insurance proceeds received with respect to the plant
                     fire at Sellers' facility in Arlington, Kentucky shall be
                     applied by Sellers in accordance with the terms of

                                       3
<PAGE>   4
                      the Senior Loan Agreement; provided, however, that if said
                      insurance proceeds exceed the amounts required to be
                      applied under the Senior Loan Agreement, then such excess
                      amount shall be paid to the Purchaser and Sterling (pro
                      rata based on the principal amounts outstanding under the
                      BOCP Note and the Sterling Note) for the purpose of
                      permanent reduction of debt under the BOCP Note and
                      Sterling Note.

           4.2       The prior written approval of the Purchaser shall be
                     required, which approval may be withheld in the Purchaser's
                     sole discretion, before Atlantic may enter into any
                     renewal, automatic or otherwise, of the Employment
                     Agreement between Atlantic Beverage Company, Inc. and Alan
                     F. Sussna, dated as of October 29, 1996, or any new or
                     replacement employment agreement with Alan F. Sussna or, if
                     Atlantic hires a new CEO or president, any employment
                     agreement with such person. Notwithstanding the foregoing,
                     if Atlantic provides the Purchaser with a written request
                     for the approval required under this Section 4.2, in
                     accordance with Section 11.13 of the Purchase Agreement,
                     then the Purchaser's failure to grant or deny such approval
                     to Atlantic in writing within 10 business days of receipt
                     of such request shall be deemed to be the Purchaser's prior
                     written approval under this Section 4.2.

           4.3       All payments or accruals owed or owing to Sterling
                     Advisors, L.P., its affiliates or employees pursuant to the
                     Sellers' Management Agreement with Sterling Advisors L.P.
                     of October 1, 2000, or any similar agreement, shall be
                     waived and canceled, and Sellers shall provide the
                     Purchaser with an acknowledgment from Sterling Advisors and
                     its principals confirming the cancellation of such
                     obligations within thirty (30) days after the date hereof.
                     No actions taken by the Sellers pursuant to this Section
                     4.3 shall be asserted by the Purchaser as a failure to
                     comply with Section 7.6 of the Purchase Agreement.

           4.4        Sellers shall use their commercially reasonable efforts,
                      subject to the fiduciary duties of Atlantic's board of
                      directors under Delaware law, to obtain replacement
                      financing for the entire remaining balance of the BOCP
                      Note on or before the end of 2001; provided, however, that
                      the failure to do so shall not constitute an Event of
                      Default.

           5. Events of Default. The occurrence of any of the following events
shall constitute an Event of Default under the Purchase Documents and, at the
Purchaser's option, shall entitle the Purchaser to exercise any or all of its
rights or remedies thereunder:

           5.1        Failure of the Sellers, or any of them, to perform any of
                      the obligations set forth in this Agreement, other than
                      Section 4.4; and

           5.2        Any breach of any representation or warranty of the
                      Sellers, or any of them, contained herein;

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<PAGE>   5
           6. No Further Waiver. Except as expressly set forth herein, nothing
contained herein shall constitute a waiver or forbearance by the Purchaser of
any other Event of Default (except for Events of Default arising out of or
relating to facts or circumstances known by the Purchaser on the date hereof),
whether now existing or hereafter arising, or waiver or modification of any
other term, condition or covenant set forth in the Purchase Documents.
Additionally, this Waiver shall not be construed as a commitment on the part of
the Purchaser to any future amendment, modification or waiver of any term,
condition or covenant set forth in the Purchase Documents.

           7. No Default. The Sellers represent and warrant that, except as set
forth in Section 1, no Event of Default has occurred and is continuing under the
Purchase Documents.

           8. Performance. The Sellers agree that, except as set forth in
Section 1, the Company will perform and observe all of the covenants,
agreements, stipulations and conditions to be performed or observed by the
Company under the Purchase Documents.

           9. Applicable Law; Jurisdiction. This Agreement shall be interpreted,
and the rights and liabilities of the parties hereto determined, in accordance
with the laws of the State of Ohio.

           10. Counterparts. This Agreement may be executed in one or more
counterparts, each of which shall be deemed an original and all of which
together shall constitute one and the same document.



                  [Remainder of page intentionally left blank]

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<PAGE>   6
           IN WITNESS WHEREOF, the Sellers and Purchaser have caused this
Agreement to be executed by their duly authorized representatives as of the day
and year first above written.

<TABLE>
<CAPTION>
<S>                                                                     <C>
Sellers:                                                                           Purchaser:

ATLANTIC PREMIUM BRANDS,                                                BANC ONE CAPITAL PARTNERS, LLC
LTD.

                                                                        By:        Banc One Capital Partners Holdings,
By:     /s/ MERRICK M. ELFMAN                                                      Ltd., Manager
    -----------------------------
Name:  Merrick M. Elfman
Its:  Chairman                                                          By:        BOCP Holdings Corporation, Manager


PREFCO CORP                                                             By:             /s/ JAMES J. HENSON
                                                                                   ---------------------------------
                                                                        Name:      James J. Henson
                                                                        Its:      Authorized Signer
By:    /s/ MERRICK M. ELFMAN
    ------------------------------------
Name:      Merrick M. Elfman
Its:       Chairman


CARLTON FOODS CORP.


By:     /s/ MERRICK M. ELFMAN
     --------------------------
Name:      Merrick M. Elfman
Its:       Chairman


RICHARDS CAJUN FOODS CORP.


By:     /s/ MERRICK M. ELFMAN
     --------------------------
Name:      Merrick M. Elfman
Its:       Chairman


GROGAN'S FARM, INC.


By:     /s/ MERRICK M. ELFMAN
     --------------------------
Name:      Merrick M. Elfman
Its:       Chairman
</TABLE>

                                       6
<PAGE>   7
POTTER SAUSAGE CO.


By:     /s/ MERRICK M. ELFMAN
     --------------------------
Name:      Merrick M. Elfman
Its:       Chairman

                                       7
<PAGE>   8
                                   EXHIBIT "A"
                           AMENDED FINANCIAL COVENANTS


           SECTION 9 FINANCIAL TESTS

           Until payment in full of the Note, the Seller shall, unless the
Purchaser waives compliance therewith in writing, meet the following Financial
Tests:

           9.1 MINIMUM FIXED CHARGE COVERAGE RATIO. The Company shall not permit
the Fixed Charge Coverage Ratio to be less than (i) the minimum ratios set forth
below as of the last day of each Quarter of 2001, (ii) .90 to 1.00 as of the
last day of each Quarter from the first Quarter of 2002 through the second
Quarter of 2003, or (iii) 1.00 to 1.00 as of the last day of each Quarter
thereafter until the Note has been paid in full:

<TABLE>
<CAPTION>
                                         1ST QUARTER              2ND QUARTER             3RD QUARTER            4TH QUARTER
                                         -----------              -----------             -----------            -----------
<S>                                      <C>                      <C>                     <C>                    <C>
Minimum Fixed Charge Coverage Ratio
                                         .85 to 1.00              .75 to 1.00             .80 to 1.00            .90 to 1.00
</TABLE>


           9.2 MINIMUM INTEREST COVERAGE RATIO. The Company shall not permit the
Interest Coverage Ratio to be less than (i) the minimum ratios set forth below
as of the last day of each Quarter of 2001, or (ii) 1.85 to 1.00 as of the last
day of each Quarter thereafter until the Note has been paid in full:

<TABLE>
<CAPTION>
                                                 1ST QUARTER              2ND QUARTER             3RD QUARTER           4TH QUARTER
                                                 -----------              -----------             -----------           -----------
<S>                                              <C>                      <C>                     <C>                   <C>
Minimum Interest Coverage Ratio                  1.60 to 1.00             1.60 to 1.00            1.75 to 1.00          1.85 to 1.00
</TABLE>


           9.3 MINIMUM SENIOR FIXED CHARGE COVERAGE RATIO. The Company shall not
permit the Senior Fixed Charge Coverage Ratio to be less than (i) the minimum
ratios set forth below as of the last day of each Quarter of 2001, or (ii) 1.05
to 1.00 as of the last day of each Quarter thereafter until the Note has been
paid in full:

<TABLE>
<CAPTION>
                                                 1ST QUARTER              2ND QUARTER             3RD QUARTER           4TH QUARTER
                                                 -----------              -----------             -----------           -----------
<S>                                              <C>                      <C>                     <C>                   <C>
Minimum Senior Fixed Charge Coverage Ratio       1.00 to 1.00              .90 to 1.00            1.00 to 1.00          1.05 to 1.00
</TABLE>

Each of the foregoing Financial Tests shall be measured on a rollup basis for
2001, i.e the trailing three months for the first Quarter, the trailing six
months for the second Quarter, the trailing nine months for the third Quarter,
and the trailing twelve months for the fourth Quarter. Beginning with the
Quarter ending March 31, 2002, the Financial Tests shall be measured on a
trailing four-quarter basis.

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<PAGE>   9
           9.4 MINIMUM STOCKHOLDERS' EQUITY. As of the end of each Quarter,
commencing in the Quarter ending March 31, 2001, the consolidated Stockholders'
equity of the Company shall not be less than $7,500,000.

           9.5 DEFINITIONS. The following terms shall have the following
definitions, for purposes of this Section 9 and for all other purposes in this
Purchase Agreement, and such definitions shall replace any definitions for such
terms in the Glossary of Terms. Capitalized terms contained in the following
definitions shall have the meanings ascribed to them in the Senior Loan
Agreement.

           (a)       FIXED CHARGE COVERAGE RATIO - for any period, the ratio of
                     (i) EBITDA minus federal and state income taxes actually
                     payable during such period, minus, with respect to any
                     period except Borrowers' first Fiscal Quarter of 2001,
                     Capital Expenditures of Borrowers on a combined and
                     consolidated basis net of Purchase Money Debt and
                     Capitalized Lease Obligations with respect thereto, to the
                     extent permitted hereunder and made during the period for
                     which the Fixed Charge Coverage Ratio is to be calculated,
                     to (ii) Fixed Charges during the period for which the Fixed
                     Charge Coverage Ratio is to be calculated.

           (b)        INTEREST COVERAGE RATIO - for any period, the ratio of (i)
                      EBITDA for such period to (ii) Cash Interest Expense for
                      such period.

           (c)       SENIOR FIXED CHARGE COVERAGE RATIO - for any period, the
                     ratio of (i) EBITDA minus actual state and federal income
                     taxes payable during such period, minus, with respect to
                     any period except Borrowers' first Fiscal Quarter of 2001,
                     Capital Expenditures of the Borrowers on a combined and
                     consolidated basis net of Purchase Money Debt and
                     Capitalized Lease Obligations with respect thereto, to the
                     extent permitted hereunder and made during the period for
                     which the Senior Fixed Charge Coverage Ratio is to be
                     calculated, to (ii) the sum of (a) Cash Interest Expense
                     attributable to Senior Loan, plus (b) payments of principal
                     due on the Term Loan or any Equipment Loan and other Senior
                     Indebtedness (including the principal component of
                     Capitalized Lease Obligations) for the period for which the
                     Senior Fixed Charge Coverage Ratio is to be calculated.

                                       9