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                                                                  Exhibit 10.44
 
                                                               Warrant No. 96-13

     NEITHER THIS WARRANT NOR THE SHARES OF COMMON STOCK ISSUABLE UPON EXERCISE
OF THIS WARRANT HAVE BEEN REGISTERED UNDER EITHER THE SECURITIES ACT OF 1933, AS
AMENDED, OR UNDER ANY STATE SECURITIES LAWS, AND THIS WARRANT CANNOT BE
EXERCISED, SOLD OR TRANSFERRED, AND THE SHARES OF COMMON STOCK ISSUABLE UPON
EXERCISE OF THIS WARRANT CANNOT BE SOLD OR TRANSFERRED, UNLESS AND UNTIL THEY
ARE SO REGISTERED OR UNLESS AN EXEMPTION IS THEN AVAILABLE.

Dated:  September 27, 1996                                  Warrant to Subscribe
                                                             for 281,907 Shares


                      EASTERN ENVIRONMENTAL SERVICES, INC.

                                    Warrant

                         To Subscribe for and Purchase
                                Common Stock of
                      EASTERN ENVIRONMENTAL SERVICES, INC.


     THIS CERTIFIES that, for value received, Willard Miller or his registered
assigns ("Holder"), is entitled to subscribe for and purchase from EASTERN
ENVIRONMENTAL SERVICES, INC., a Delaware corporation ("Company"), at an exercise
price per share of $6.75 (initially and as adjusted, if at all, pursuant to the
terms and conditions of this Warrant, the "Exercise Price"), 281,907 fully paid
                                           --------------                      
and nonassessable shares of Company's common stock, par value $.01 per share
(the "Common Stock").  This Warrant may be exercised, in whole or in part, in
      ------------                                                           
six (6) blocks consisting of one (1) block of 46,168 shares, one (1) block of
35,739 shares and four (4) blocks of 50,000 shares (individually a "Block" and
collectively the "Blocks").  The Block of 46,168 may be exercised on and after
October 27, 1996.  The Block of 35,739 may be exercised on and after December
27, 1996.  The first Block of 50,000 may be exercised on or after September 27,
1997, with an additional Block of 50,000 being exercisable on September 27 of
each successive calendar year with the final Block of 50,000 being exercisable
on and after September 27, 2000.  Notwithstanding the prior sentence, all Blocks
shall be exercisable upon a Change of Control, as hereinafter defined.

     For purposes of this Warrant, a "Change of Control" shall mean the
occurrence of the following events:  (i) the acquisition in one or more
transactions by any "Person", (as the term "Person" is used for purposes of
Sections 13(d) or 14(d) of the Securities Exchange Act of 1934, as amended ("the
1934 Act")) of "Beneficial Ownership" (as the term beneficial ownership is used
for purposes of Rule 13d-3 promulgated under the 1934 Act) of fifty percent
(50%) or more of the combined voting power of the Company's then outstanding
voting securities (the "Voting Securities").  For purposes of this
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paragraph, the Voting Securities acquired directly from the Company by any
Person shall be excluded from the determination of such Person's Beneficial
Ownership of Voting Securities (but such Voting Securities shall be included in
the calculation of the total number of Voting Securities then outstanding).  For
purposes of this paragraph, the acquisition of the holder of this Warrant of the
Beneficial Ownership of 50% percent or more of the Voting Securities shall not
be a Change of Control; or (ii) the current directors of the Company, Louis D.
Paolino, Jr., Kenneth Leung and George Moorehead, no longer constitute a
majority of the Company's Board of Directors.  No exercise of any Blocks may
occur after 5:00 p.m. Eastern time on the tenth anniversary of the date hereof.

     This Warrant is subject to the following provisions, terms and conditions:

     1.  Exercise; Payment.  The rights represented by this Warrant may be
         -----------------                                                
exercised by Holder, in whole or in part, by the surrender of this Warrant at
the principal office of Company properly endorsed and accompanied by payment to
Company of the Exercise Price for that number of shares of Common Stock sought
to be purchased (the "Exercised Shares"), in the manner provided below. Company
                      ----------------                                         
agrees that (a) shares purchased upon exercise of this Warrant shall be and are
deemed to be issued to Holder as the record owner of such shares as of the close
of business on the date on which this Warrant shall have been surrendered and
payment made for such shares as provided herein, and (b) certificates for the
shares of stock so purchased shall be delivered to Holder as promptly as
reasonably practicable following any exercise of this Warrant, and unless this
Warrant shall have been exercised in full, or shall have expired, a new Warrant
representing the number of shares with respect to which this Warrant shall not
yet have been exercised, shall also be delivered to Holder.

     Holder may pay the Exercise Price for any Exercised shares in one or a
combination of the following methods:

     (a) By delivering cash, check, money order or wire transfer of funds to the
Company in the amount of the Exercise Price of the Exercised Shares; or

     (b) By surrendering to the Company shares of Common Stock having a Fair
Market Value (as measured on the date of exercise of the Exercised Shares) equal
to the Exercise Price of the Exercised Shares.

     2.  Shares to be Fully Paid; Reservation.  Company covenants and agrees
         ------------------------------------                               
that all shares which may be issued upon the exercise of the rights represented
by this Warrant will, upon issuance and payment therefor in accordance with
Section 1 above, be fully paid and nonassessable and free from all taxes, liens
and charges with respect to the issue thereof; and without limiting the
generality of the foregoing, Company covenants and agrees that it will from

                                       2
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time to time take all such action as may be required to assure that the par
value per share of the Common Stock is at all times equal to or less than the
then effective Exercise Price per share of Common Stock issuable pursuant to
this Warrant.  Company further covenants and agrees that when the rights
represented by this Warrant may be exercised, Company will at all times
thereafter have authorized, and reserved for the purpose of issue or transfer
upon exercise of the subscription rights evidenced by this Warrant, a sufficient
number of shares of its Common Stock to provide for the exercise of the rights
represented by this Warrant.

     3.  Reorganization.  In case of any reorganization of Company, or any other
         --------------                                                         
corporation the stock or securities of which are at the time deliverable on the
exercise of this Warrant, or in case Company or such other corporation shall
consolidate with or merge into another corporation, or convey all or
substantially all of its assets to another corporation, or liquidate, Holder,
upon the exercise hereof and upon the payment of the Exercise Price provided
above, shall be entitled to receive, in lieu of the shares called for under this
Warrant, the stock or other securities or property to which Holder would have
been entitled upon the consummation of such reorganization, consolidation,
merger, conveyance, or liquidation if Holder had purchased the shares called for
hereby immediately prior thereto; and in such case, the provisions of this
Warrant shall be applicable to the shares of stock or other securities or
property thereafter deliverable upon the exercise of this Warrant.  In the case
of the partial exercise of this Warrant under such circumstances, the number of
shares of stock or other securities or property which would have been receivable
upon the full exercise of this Warrant, and the Exercise Price payable therefor,
shall be proportionately reduced.

     4.  No Rights as Shareholder.  Until the valid exercise of this Warrant,
         ------------------------                                            
the holder hereof shall not be entitled to any voting right or other rights as a
shareholder of Company with respect to this Warrant.

     5.  Transfer of Warrants.  Subject to Section 7 hereof, this Warrant and
         --------------------                                                
all rights hereunder are transferable, in whole or in part, without charge to
the Holder, at the office or agency of Company referred to in Section 1 by the
Holder in person or by duly authorized attorney, upon surrender of this Warrant
properly endorsed.  Each taker and holder of this Warrant, by taking or holding
the same, consents and agrees that this Warrant, when endorsed in blank, shall
be deemed negotiable, and that the holder hereof, when this Warrant shall have
been so endorsed, may be treated by Company and all other persons dealing with
this Warrant as the absolute owner hereof for any purpose and as the person
entitled to exercise the rights represented by this Warrant, or to the transfer
hereof on the books of Company, any notice to the contrary notwithstanding; but
until such transfer on such books, Company may treat the registered holder
hereof as the owner for all purposes.

                                       3
<PAGE>
 
     6.  Fractional Interests.  Company shall not be required to issue
         --------------------                                         
fractional shares of Common Stock upon the exercise of this Warrant.  If any
fraction of a share of Common Stock would, except for the provisions of this
Section 6, be issuable upon the exercise of this Warrant (or specified portion
thereof), Company shall pay an amount in cash equal to the Fair Market Value (as
defined below) of such fraction of a Common Share on the business day prior to
the date of such exercise.  As used in this Agreement, the "Fair Market Value"
                                                            ----------------- 
of the Common Stock shall be the closing price of the Common Stock on the date
of determination on the principal stock market or quotation system on which the
Common Stock is then traded; provided, however, if the Common Stock is not, as
                             --------  -------                                
of the date of determination of the Fair Market Value, traded on a recognized
public trading market or quoted on a recognized quotation system, then the Fair
Market Value shall be determined by  Company on the basis of such valuation as
it considers appropriate.

     7.  Compliance With Securities Laws.  By acquiring this Warrant from
         -------------------------------                                 
Company on the date hereof, the Holder hereby agrees, acknowledges, covenants,
represents and warrants as follows:

         (a)  This Warrant and the shares of Common Stock issuable upon exercise
hereof have not been registered under the Securities Act of 1933, as amended
(the "Securities Act"), or qualified or registered under any state securities
laws which may be applicable. Holder understands that this Warrant and such
shares of Common Stock have been and will be issued and sold hereunder in
transactions exempt from the registration or qualification requirements of the
Securities Act and applicable state securities laws and Holder acknowledges that
reliance on and the availability of said exemptions is predicated in part on the
accuracy of Holder's representations and warranties herein.

         (b)  Holder represents and warrants that it is acquiring this Warrant
for its own account, for purposes of investment, and not with a view to, or for
sale in connection with, any distribution thereof within the meaning of the
Securities Act and the rules and regulations promulgated thereunder. Holder
represents, warrants and agrees that it will not sell, exercise, transfer or
otherwise dispose of this Warrant (or any interest therein) or any of the Common
Stock purchasable upon exercise hereof, except pursuant to (i) an effective
registration statement under the Securities Act and applicable state securities
laws or (ii) an opinion of counsel, satisfactory to Company, that an exemption
from registration under the Securities Act and such laws is available. Holder
further acknowledges and agrees that Company is not required, legally or
contractually, so to register or qualify the Warrant or such Common Stock or to
take any action to make such an exemption available. Holder understands that
Company will be relying upon the truth and accuracy of the representations and
warranties contained in this Section 7 in issuing this Warrant and such Common
Stock without first registering the issuance thereof under the Securities Act or
qualifying or registering the

                                       4
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issuance thereof under any state securities laws that may be applicable.

     (c)  Holder acknowledges that (i) there is not now, and there will not be
in the future, any public market for the Warrant, (ii) although there currently
is a public trading market for the Common Stock, there can be no assurance that
any such market will be sustained, and (iii) there can be no assurance that
Holder will be able to liquidate its investment in Company.  Holder represents
and warrants that it is familiar with and understands the terms and conditions
of Rule 144 promulgated under the Securities Act.

     (d)  Holder represents and warrants to Company that (i) it has such
knowledge and experience in financial and business matters as is necessary to
enable it to evaluate the merits and risks of any investments in Company and is
not utilizing any other person to be a purchaser representative in connection
with evaluation of such merits and risks; and (ii) it has no need for liquidity
in an investment in Company and is able to bear the risk of that investment for
an indefinite period and to afford a complete loss thereof.

     (e)  Holder represents and warrants that it has had access to, and has been
furnished with, all of the information it has requested from Company and has had
an opportunity to review the books and records of Company and to discuss with
management and members of the board of directors of Company the business and
financial affairs of Company.

     (f)  Holder agrees that at the time of each exercise of this Warrant,
unless the issuance of shares of Common Stock issuable thereupon is pursuant to
an effective registration statement under the Securities Act, Holder will
provide Company with a letter embodying the representations and warranties set
forth in subsections (b) through (e), in form and substance satisfactory to
Company, and agrees that the certificate(s) representing any shares issued to it
upon any exercise of this Warrant may bear such restrictive legend as Company
may deem necessary to reflect the restricted status of such shares under the
Securities Act unless Company shall have received from Holder an opinion of
counsel to Holder, reasonably satisfactory in form and substance to Company,
that such restrictive legend is not required. If such legend is placed on such
certificate(s), before consenting to the removal of such legend and the transfer
of such shares, unless the request to remove such legend is made in connection
with a sale or transfer of the shares represented by such certificate in a
transaction registered under Section 5 of the Securities Act, Company may insist
upon the delivery to it of an opinion from counsel to Holder, reasonably
satisfactory in form and substance to Company, that the contemplated transfer
does not constitute a violation of the Securities Act.


                                       5
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     8.  Notice.  Company covenants and agrees to give notice in writing to
         ------                                                            
Holder at least 10 days prior to (or, if later, then as soon as reasonably
practicable prior to) any action contemplated which would affect the per share
Exercise Price, or number of shares purchasable upon exercise of this Warrant;
provided, however, any failure of Company to provide such notice shall not
--------  -------                                                         
affect the validity of any action by Company.  Any notice, request or other
communication provided for under this Warrant shall be given in writing,
delivered by hand, by overnight United States Mail, return receipt requested,
postage prepaid, or through a reputable courier service (such as Federal
Express) and shall be addressed to Company or to the Holder at the address shown
below, unless notice of a change in address is furnished in accordance with this
paragraph:

     If to Company:

          Eastern Environmental Services, Inc.
          1000 Crawford Place                
          Suite 101                          
          Mt. Laurel, NJ 08054               
          Attn:  Chief Financial Officer      

     If to Holder:

          Willard Miller       
          230 Orono Place      
          Sommerdale, NJ 08083  

     9.  Descriptive Headings and Governing Law.  The descriptive headings of
         --------------------------------------                              
the several paragraphs of this Warrant are inserted for convenience only and do
not constitute a part of this Warrant. This Warrant is being delivered and is
intended to be performed in the Commonwealth of Pennsylvania and shall be
construed and enforced in accordance with, and the rights of the parties shall
be governed by, the law of such state.

     IN WITNESS WHEREOF, Eastern Environmental Services, Inc. has caused this
Warrant to be signed by its duly authorized officers under its corporate seal,
this 27th day of September, 1996.


                                  EASTERN ENVIRONMENTAL SERVICES, INC. 
                                                                       
                                                                       
                                  By:  /s/ Robert M. Kramer            
                                     ----------------------------------
                                  Title: Vice President                
                                         ------------------------------
                                                                       
                                  Print Name: Robert M. Kramer         
                                              ------------------------- 

                                       6
<PAGE>
 
                              ELECTION TO PURCHASE
                              --------------------

     The undersigned Holder hereby irrevocable elects to exercise the within
Warrant to purchase (___________)* Shares of Common Stock issuable upon exercise
thereof to and requests that certificates for such Shares be issued in 
his/her/its name and delivered to him/her/it at the following
address:________________________________________________________________________
________________________________________________________________________________
_______________________________________________________________________________.


Date:_________________

________________________________________________________________________________
                                Signature(s)**



____________________________

*  If the Warrant is to be exercised or transferred in its entirety, insert the
word "All" before "Shares"; otherwise insert the number of shares then
purchasable on the exercise thereof as to which transferred or exercised.  If
such Warrants shall not be transferred or exercised to purchase all shares
purchasable upon exercise thereof, that a new Warrant to purchase the balance of
such shares be issued in the name of, and delivered to, the Holder at the
address stated below.

**  Signature(s) must conform exactly to the name(s) of the Holder as set forth
on the first page of this Warrant.
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                                   ASSIGNMENT
                                   ----------


     FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers the
within Warrant to the extent of (________)* Shares purchasable upon exercise
thereof to ____________________________, whose address is ______________________
______________________________________________ and hereby irrevocably constitute
and appoint ____________________ his/her/its Attorney to transfer said Warrant
on the book of the Company, with full power of substitution.


Date:_______________________


________________________________________________________________________________
                                Signature(s)**



__________________________

*  If the Warrant is to be exercised or transferred in its entirety, insert the
word "All" before "Shares"; otherwise insert the number of shares then
purchasable on the exercise thereof as to which transferred or exercised.  If
such Warrants shall not be transferred or exercised to purchase all shares
purchasable upon exercise thereof, that a new Warrant to purchase the balance of
such shares be issued in the name of, and delivered to, the Holder at the
address stated below.

**  Signature(s) must conform exactly to the name(s) of the Holder as set forth
on the first page of this Warrant.