<PAGE>

                                                                   EXHIBIT 10.40


                            LEASE SUPPLEMENT NO. 1

        THIS LEASE SUPPLEMENT NO. 1 (this "Lease Supplement") dated as of June
15, 1999, between HANOVER EQUIPMENT TRUST 1999A, a Delaware business trust, as
lessor (the "Lessor"), and HANOVER COMPRESSOR COMPANY, a Delaware corporation,
as lessee (the "Lessee").

        WHEREAS, the Lessor is the owner of the Equipment described on Schedule
I hereto (the "Leased Equipment") and wishes to lease the same to the Lessee;

        NOW, THEREFORE, in consideration of the premises and the mutual
agreements herein contained and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties hereto
agree as follows:

        1. Definitions; Rules of Usage. For purposes of this Lease Supplement,
capitalized terms used herein and not otherwise herein shall have the meanings
assigned to them in Annex A to the Participation Agreement, dated as of June 15,
1999, among the Lessee, the Lessor, the Investors, the Agent, and the Lenders,
as it may be amended, supplemented or otherwise modified from time to time.

        2. The Equipment. Attached hereto as Schedule I is the description of
the Leased Equipment. Effective upon the execution and delivery of this Lease
Supplement by the Lessor and the Lessee, the Leased Equipment shall be subject
to the terms and provisions of the Lease.

        3. Ratification. Except as specifically modified hereby, the terms and
provisions of the Lease are hereby ratified and confirmed and remain in full
force and effect.

        4. Original Lease Supplement. The single executed original of this Lease
Supplement marked "THIS COUNTERPART IS THE ORIGINAL EXECUTED COUNTERPART" on the
signature page thereof and containing the receipt of the Agent therefor on or
following the signature page thereof shall be the Original Executed Counterpart
of this Lease Supplement (the "Original Executed Counterpart"). To the extent
that this Lease Supplement constitutes chattel paper, as such term is defined in
the Uniform Commercial Code as in effect in any applicable jurisdiction, no
security interest in this Lease Supplement may be created through the transfer
or possession of any counterpart other than the Original Executed Counterpart.

        5. GOVERNING LAW. THIS LEASE HAS BEEN DELIVERED IN, AND SHALL IN ALL
RESPECTS BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE
OF NEW YORK APPLICABLE TO AGREEMENTS MADE AND TO BE PERFORMED ENTIRELY WITHIN
SUCH STATE.
<PAGE>

        6. Counterpart Execution. This Lease Supplement may be executed in any
number of counterparts and by each of the parties hereto in separate
counterparts, all such counterparts together constituting but one and the same
instrument.

        7. Recordation. The Lessor and the Lessee agree that a memorandum of
this Lease Supplement No. 1 shall be recorded at the Lessee's sole cost and
expense as required by the Lease.
<PAGE>

        IN WITNESS WHEREOF, the parties have caused this Lease Supplement No. 1
be duly executed and delivered as of the date first above written.

                                     HANOVER COMPRESSOR COMPANY

                                     By: ___________________________________
                                         Name:
                                         Title:

                                     HANOVER EQUIPMENT TRUST 1999A

                                     By: Wilmington Trust Company, not in its
                                     individual capacity but solely as Trustee

                                     By: _____________________________
                                         Name:
                                         Title:
<PAGE>

        Receipt of this original counterpart of the foregoing Lease Supplement
is hereby acknowledged on this 15th day of June, 1999.

                                       THE CHASE MANHATTAN BANK, as the Agent
                                       for the Lenders

                                       By: ___________________________________
                                           Name:
                                           Title: