<PAGE>
 
                                                                    EXHIBIT 4(i)

                          CERTIFICATE OF DESIGNATION

                                       of

                         SERIES A JUNIOR PARTICIPATING
                                PREFERRED STOCK

                                       of

                                THE BIBB COMPANY

                        (Pursuant to Section 151 of the
               General Corporation Law of the State of Delaware)


     The Bibb Company, a corporation organized and existing under the General
Corporation Law of the State of Delaware (hereinafter called the "Corporation"),
DOES HEREBY CERTIFY:

     That, pursuant to authority vested in the Board of Directors of the
Corporation by its Certificate of Incorporation, and pursuant to the provisions
of Section 151 of the General Corporation Law, the Board of Directors of the
Corporation has adopted the following resolution providing for the issuance of a
series of Preferred Stock:

     RESOLVED, that pursuant to the authority expressly granted to and vested in
the Board of Directors of the Corporation (hereinafter called the "Board of
Directors" or the "Board") by the Certificate of Incorporation of the
Corporation, a series of Preferred Stock, par value $.01 per share (the
"Preferred Stock"), of the Corporation be, and it hereby is, created, and that
the designation and amount thereof and the powers, designations, preferences and
relative, participating, optional and other special rights of the shares of such
series, and the qualifications, limitations or restrictions thereof are as
follows:

                           I.  Designation and Amount
                               ----------------------

     The shares of such series will be designated as Series A Junior
Participating Preferred Stock (the "Series A Preferred") and the number of
shares constituting the Series A Preferred is 250,000.  Such number of shares
may be increased or decreased by resolution of the Board; provided, however,
                                                          --------  ------- 
that no decrease will reduce the number of shares of Series A Preferred to a
number less than the number of shares then outstanding plus the number of shares
reserved for issuance upon the exercise of outstanding options, rights or
warrants or upon the conversion of any outstanding securities issued by the
Corporation convertible into Series A Preferred.

                        II.  Dividends and Distributions
                             ---------------------------

     (a) Subject to the rights of the holders of any shares of any series of
Preferred Stock ranking prior to the Series A Preferred with respect to
dividends, the holders of shares of Series A Preferred, in preference to the
holders of Common Stock, par value $.01 per share (the "Common Stock"), of the
Corporation, and of any other junior stock, will be entitled to receive, when,
as
<PAGE>
 
and if declared by the Board out of funds legally available for the purpose,
dividends payable in cash (except as otherwise provided below) on such dates as
are from time to time established for the payment of dividends on the Common
Stock (each such date being referred to herein as a "Dividend Payment Date"),
commencing on the first Dividend Payment Date after the first issuance of a
share or fraction of a share of Series A Preferred (the "First Dividend Payment
Date"), in an amount per share (rounded to the nearest cent) equal to the
greater of (i) $1.00 or (ii) subject to the provision for adjustment hereinafter
set forth, one hundred times the aggregate per share amount of all cash
dividends, and one hundred times the aggregate per share amount (payable in
kind) of all non-cash dividends, other than a dividend payable in shares of
Common Stock or a subdivision of the outstanding shares of Common Stock (by
reclassification or otherwise), declared on the Common Stock since the
immediately preceding Dividend Payment Date or, with respect to the First
Dividend Payment Date, since the first issuance of any share or fraction of a
share of Series A Preferred.  In the event that the Corporation at any time (i)
declares a dividend on the outstanding shares of Common Stock payable in shares
of Common Stock, (ii) subdivides the outstanding shares of Common Stock, (iii)
combines the outstanding shares of Common Stock into a smaller number of shares,
or (iv) issues any shares of its capital stock in a reclassification of the
outstanding shares of Common Stock (including any such reclassification in
connection with a consolidation or merger in which the Corporation is the
continuing or surviving corporation), then, in each such case and regardless of
whether any shares of Series A Preferred are then issued or outstanding, the
amount to which holders of shares of Series A Preferred would otherwise be
entitled immediately prior to such event under clause (ii) of the preceding
sentence will be adjusted by multiplying such amount by a fraction, the
numerator of which is the number of shares of Common Stock outstanding
immediately after such event and the denominator of which is the number of
shares of Common Stock that were outstanding immediately prior to such event.

     (b) The Corporation will declare a dividend on the Series A Preferred as
provided in the immediately preceding paragraph immediately after it declares a
dividend on the Common Stock (other than a dividend payable in shares of Common
Stock).  Each such dividend on the Series A Preferred will be payable
immediately prior to the time at which the related dividend on the Common Stock
is payable.

     (c) Dividends will accrue on outstanding shares of Series A Preferred from
the Dividend Payment Date next preceding the date of issue of such shares,
unless (i) the date of issue of such shares is prior to the record date for the
First Dividend Payment Date, in which case dividends on such shares will accrue
from the date of the first issuance of a share of Series A Preferred or (ii) the
date of issue is a Dividend Payment Date or is a date after the record date for
the determination of holders of shares of Series A Preferred entitled to receive
a dividend and before such Dividend Payment Date, in either of which events such
dividends will accrue from such Dividend Payment Date.  Accrued but unpaid
dividends will cumulate from the applicable Dividend Payment Date but will not
bear interest.  Dividends paid on the shares of Series A Preferred in an amount
less than the total amount of such dividends at the time accrued and payable on
such shares will be allocated pro rata on a share-by-share basis among all such
shares at the time outstanding.  The Board may fix a record date for the
determination of holders of shares of Series A Preferred entitled to receive
payment of a dividend or distribution declared thereon, which record date will
be not more than 60 calendar days prior to the date fixed for the payment
thereof.

                                       2
<PAGE>
 
                              III.  Voting Rights
                                    -------------

     The holders of shares of Series A Preferred will have the following voting
rights:

          (a) Subject to the provision for adjustment hereinafter set forth,
     each share of Series A Preferred will entitle the holder thereof to one
     hundred votes on all matters submitted to a vote of the stockholders of the
     Corporation.  In the event the Corporation at any time (i) declares a
     dividend on the outstanding shares of Common Stock payable in shares of
     Common Stock, (ii) subdivides the outstanding shares of Common Stock, (iii)
     combines the outstanding shares of Common Stock into a smaller number of
     shares, or (iv) issues any shares of its capital stock in a
     reclassification of the outstanding shares of Common Stock (including any
     such reclassification in connection with a consolidation or merger in which
     the Corporation is the continuing or surviving corporation), then, in each
     such case and regardless of whether any shares of Series A Preferred are
     then issued or outstanding, the number of votes per share to which holders
     of shares of Series A Preferred would otherwise be entitled immediately
     prior to such event will be adjusted by multiplying such number by a
     fraction, the numerator of which is the number of shares of Common Stock
     outstanding immediately after such event and the denominator of which is
     the number of shares of Common Stock that were outstanding immediately
     prior to such event.

          (b) Except as otherwise provided herein, in any other Preferred Stock
     Designation creating a series of Preferred Stock or any similar stock, or
     by law, the holders of shares of Series A Preferred and the holders of
     shares of Common Stock and any other capital stock of the Corporation
     having general voting rights will vote together as one class on all matters
     submitted to a vote of stockholders of the Corporation.

          (c) Except as set forth in the Certificate of Incorporation or herein,
     or as otherwise provided by law, holders of shares of Series A Preferred
     will have no voting rights.

                           IV.  Certain Restrictions
                                --------------------

     (a) Whenever dividends or other dividends or distributions payable on the
Series A Preferred are in arrears, thereafter and until all accrued and unpaid
dividends and distributions, whether or not declared, on shares of Series A
Preferred outstanding have been paid in full, the Corporation will not:

          (i) Declare or pay dividends, or make any other distributions, on any
     shares of stock ranking junior (either as to dividends or upon liquidation,
     dissolution or winding up) to the shares of Series A Preferred;

          (ii) Declare or pay dividends, or make any other distributions, on any
     shares of stock ranking on a parity (either as to dividends or upon
     liquidation, dissolution, or winding up) with the shares of Series A
     Preferred, except dividends paid ratably on the shares of Series A
     Preferred and all such parity stock on which dividends are payable or in

                                       3
<PAGE>
 
     arrears in proportion to the total amounts to which the holders of all such
     shares are then entitled;

          (iii)  Redeem, purchase or otherwise acquire for consideration shares
     of any stock ranking junior (either as to dividends or upon liquidation,
     dissolution or winding up) to the shares of Series A Preferred; provided,
                                                                     -------- 
     however, that the Corporation may at any time redeem, purchase or otherwise
     -------                                                                    
     acquire shares of any such junior stock in exchange for shares of any stock
     of the Corporation ranking junior (either as to dividends or upon
     dissolution, liquidation or winding up) to the shares of Series A
     Preferred; or

          (iv) Redeem, purchase or otherwise acquire for consideration any
     shares of Series A Preferred, or any shares of stock ranking on a parity
     with the shares of Series A Preferred, except in accordance with a purchase
     offer made in writing or by publication (as determined by the Board) to all
     holders of such shares upon such terms as the Board, after consideration of
     the respective annual dividend rates and other relative rights and
     preferences of the respective series and classes, may determine in good
     faith will result in fair and equitable treatment among the respective
     series or classes.

   (b) The Corporation will not permit any majority-owned subsidiary of the
Corporation to purchase or otherwise acquire for consideration any shares of
stock of the Corporation unless the Corporation could, under paragraph (a) of
this Article IV, purchase or otherwise acquire such shares at such time and in
such manner.

                             V.  Reacquired Shares
                                 -----------------

   Any shares of Series A Preferred purchased or otherwise acquired by the
Corporation in any manner whatsoever will be retired and canceled promptly after
the acquisition thereof.  All such shares will upon their cancellation become
authorized but unissued shares of Preferred Stock and may be reissued as part of
a new series of Preferred Stock subject to the conditions and restrictions on
issuance set forth herein, in the Certificate of Incorporation of the
Corporation, or in any other Preferred Stock Designation creating a series of
Preferred Stock or any similar stock or as otherwise required by law.

                  VI.  Liquidation, Dissolution or Winding Up
                       --------------------------------------

   Upon any liquidation, dissolution or winding up of the Corporation, no
distribution will be made (a) to the holders of shares of stock ranking junior
(either as to dividends or upon liquidation, dissolution, or winding up) to the
shares of Series A Preferred unless, prior thereto, the holders of shares of
Series A Preferred have received $100 per share, plus an amount equal to accrued
and unpaid dividends and distributions thereon, whether or not declared, to the
date of such payment; provided, however, that the holders of shares of Series A
                      --------  -------                                        
Preferred will be entitled to receive an aggregate amount per share, subject to
the provision for adjustment hereinafter set forth, equal to one hundred times
the aggregate amount to be distributed per share to holders of shares of Common
Stock or (b) to the holders of shares of stock ranking on a parity (either as to
dividends or upon liquidation, dissolution, or winding up) with the shares of
Series A Preferred, except distributions made ratably on the shares of Series A
Preferred and all such parity stock in proportion to the total amounts to which
the holders of all such shares are entitled upon such

                                       4
<PAGE>
 
liquidation, dissolution, or winding up.  In the event the Corporation at any
time (i) declares a dividend on the outstanding shares of Common Stock payable
in shares of Common Stock, (ii) subdivides the outstanding shares of Common
Stock, (iii) combines the outstanding shares of Common Stock into a smaller
number of shares, or (iv) issues any shares of its capital stock in a
reclassification of the outstanding shares of Common Stock (including any such
reclassification in connection with a consolidation or merger in which the
Corporation is the continuing or surviving corporation), then, in each such case
and regardless of whether any shares of Series A Preferred are then issued or
outstanding, the aggregate amount to which each holder of shares of Series A
Preferred would otherwise be entitled immediately prior to such event under the
proviso in clause (a) of the preceding sentence will be adjusted by multiplying
such amount by a fraction, the numerator of which is the number of shares of
Common Stock outstanding immediately after such event and the denominator of
which is the number of shares of Common Stock that were outstanding immediately
prior to such event.

                       VII.  Consolidation, Merger, Etc.
                             ---------------------------

   In the event that the Corporation enters into any consolidation, merger,
combination or other transaction in which the shares of Common Stock are
exchanged for or changed into other stock or securities, cash and/or any other
property, then, in each such case, each share of Series A Preferred will at the
same time be similarly exchanged for or changed into an amount per share,
subject to the provision for adjustment hereinafter set forth, equal to one
hundred times the aggregate amount of stock, securities, cash and/or any other
property (payable in kind), as the case may be, into which or for which each
share of Common Stock is changed or exchanged.  In the event the Corporation at
any time (a) declares a dividend on the outstanding shares of Common Stock
payable in shares of Common Stock, (b) subdivides the outstanding shares of
Common Stock, (c) combines the outstanding shares of Common Stock in a smaller
number of shares, or (d) issues any shares of its capital stock in a
reclassification of the outstanding shares of Common Stock (including any such
reclassification in connection with a consolidation or merger in which the
Corporation is the continuing or surviving corporation), then, in each such case
and regardless of whether any shares of Series A Preferred are then issued or
outstanding, the amount set forth in the preceding sentence with respect to the
exchange or change of shares of Series A Preferred will be adjusted by
multiplying such amount by a fraction, the numerator of which is the number of
shares of Common Stock outstanding immediately after such event and the
denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.

                               VIII.  Redemption
                                      ----------

   The shares of Series A Preferred are not redeemable.

                                   IX.  Rank
                                        ----

   The Series A Preferred rank, with respect to the payment of dividends and the
distribution of assets, junior to all other series of the Corporation's
Preferred Stock.

                                       5
<PAGE>
 
                                 X.  Amendment
                                     ---------

     Notwithstanding anything contained in the Certificate of Incorporation
of the Corporation to the contrary and in addition to any other vote required by
applicable law, the Certificate of Incorporation of the Corporation may not be
amended in any manner that would materially alter or change the powers,
preferences or special rights of the Series A Preferred so as to affect them
adversely without the affirmative vote of the holders of at least 80% of the
outstanding shares of Series A Preferred, voting together as a single series.

                                       6
<PAGE>
 
      IN WITNESS WHEREOF, this Certificate of Designation is executed and
attested on behalf of the Corporation this 13th day of October, 1997.


                                     /s/ Charles R. Tutterow
                                    -----------------------------------------
                                    Name:  Charles R. Tutterow
                                    Title: Vice President



/s/ Neal J. McGrail     
-------------------------------
Neal J. McGrail     
Assistant Secretary 

                                       7