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                                                                     EXHIBIT 4.1


                                LIMITED GUARANTY


                 THIS LIMITED GUARANTY ("Guaranty"), is made and entered into
as of September 24, 1998 by DOUGLAS A. P. HAMILTON ("Guarantor"), for the
benefit of COMPASS BANK, a Texas state chartered banking institution ("Bank").


                              W I T N E S S E T H:


                 WHEREAS, on the date hereof, Bank has advanced or will advance
certain funds to CARRIZO OIL & GAS, INC., a Texas corporation ("Borrower")
pursuant to the Fourth Amendment of even date herewith to that certain First
Amended and Restated Loan Agreement dated August 28, 1997, as amended by the
First Amendment thereto dated December 23, 1997, the Second Amendment thereto
dated December 30, 1997 and the Third Amendment thereto dated July 30, 1998
(the "Loan Agreement"), specifically including the indebtedness evidenced by
that certain term promissory note dated of even date herewith, executed by
Borrower and payable to Bank, in the principal amount of $7,000,000.00 and all
other notes given in substitution therefor or in modification, renewal or
extension thereof in whole or in part (the "Second Term Note");

                 WHEREAS, as a condition to Bank's entry into said Fourth
Amendment and its advance of funds to Borrower thereunder, Guarantor has agreed
to enter into this Guaranty of certain indebtedness owed or to be owed by
Borrower to Bank; and

                 WHEREAS, Guarantor will directly and indirectly benefit from
the Second Term Loan, as defined in the Loan Agreement, as amended by the
Fourth Amendment and evidenced by the Second Term Note.

                 NOW, THEREFORE, for and in consideration of the premises and
the extension of credit by Bank to Borrower pursuant to the Loan Agreement, and
for TEN AND NO/100 DOLLARS ($10.00) and other good and valuable consideration,
the receipt and sufficiency of which are hereby acknowledged, and to induce
Bank to execute the Fourth Amendment, Bank and Guarantor hereby agree as
follows:

                 1.       Guarantor unconditionally guarantees the prompt
payment to Bank of the following (the "Guaranteed Indebtedness"):

         (a)     Any and all indebtedness, obligations (including reimbursement
                 obligations) and liabilities of Borrower to Bank now existing
                 or hereafter incurred in connection with or incident to the
                 Second Term Loan, under or arising out of or in connection
                 with any documents executed in connection with any
                 indebtedness of Borrower to Bank in connection with the Second
                 Term Loan
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                 or any promissory note or notes executed by Borrower at any
                 time in connection with the Second Term Loan, whether for
                 principal, interest, penalty interest, fees, expenses or
                 otherwise, including, without limitation, all sums, principal,
                 accrued interest and other amounts owing with respect to the
                 Second Term Note, together with any and all renewals,
                 extensions and/or rearrangements thereof, whether with or
                 without notice to Guarantor;

         (b)     All interest, charges, expenses, attorneys' or other fees and
                 any other sums payable to or incurred by the Bank in
                 connection with the execution, administration or enforcement
                 of the Bank's rights and remedies under the Second Term Note;
                 and

         (c)     All post-petition interest on the Guaranteed Indebtedness in
                 the event of a bankruptcy or insolvency of the Borrower.

Provided, however, that Guarantor's obligation hereunder shall never exceed
$3,500,000.00.  Guarantor shall at all times maintain at least $4,000,000 in
Liquid Assets.  To evidence such maintenance of Liquid Assets, Guarantor shall
deliver to Bank, on or before the forty-fifth (45th) day after the end of each
calendar quarter, a Certificate of Liquidity in the form attached hereto as
Exhibit "A", certifying the value of such Guarantor's Liquid Assets effective
as of the end of each calendar quarter.  "Liquid Assets" shall mean Cash on
hand and balances in checking accounts available for immediate withdrawal, the
value, from time to time, of short-term, highly liquid investments that are
readily convertible to Cash, such as treasury bills, commercial paper and money
market funds, and the value, from time to time, of unrestricted shares of stock
that are publicly traded on the New York Stock Exchange, the American Stock
Exchange, or NASDAQ, and otherwise acceptable to the Bank, but only to the
extent the foregoing are free from all liens, claims and encumbrances,
including liens or security interests in favor of the Bank.  "Cash" shall mean
legal tender of the United States of America.

                 2.       If the Guaranteed Indebtedness is not paid by
Guarantor when due, as required herein, and this Guaranty is placed in the
hands of an attorney for collection, or if this Guaranty is enforced by suit or
through the Bankruptcy Court or through any judicial proceedings, Guarantor
shall pay to Bank an amount equal to its reasonable attorneys' fees and
collection costs incurred by Bank in the collection of the Guaranteed
Indebtedness.

                 3.       This is an absolute, complete and continuing
Guaranty, and no notice of the Guaranteed Indebtedness or any extension of
credit already or hereafter contracted by or extended to Borrower need be given
to Guarantor, nor shall anything herein contained be a limitation upon the
amount of credit which may be extended to Borrower, the numbers of transactions
with Borrower, repayments by Borrower to Bank, or the allocation by Bank of
repayment by Borrower, it being the understanding of the Guarantor that
Guarantor's liability shall continue hereunder so long as any of the Guaranteed
Indebtedness remains unpaid.  Borrower and Bank may rearrange, increase,
decrease, extend and/or renew the Guaranteed Indebtedness without notice to
Guarantor and in such





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event Guarantor will remain fully bound hereunder on the Guaranteed
Indebtedness.  The obligations of Guarantor hereunder shall not be released,
impaired or diminished by any amendment, modification or alteration of the Loan
Agreement or the Second Term Note.  Guarantor expressly waives all notices of
any kind, presentment for payment, demand for payment, protest, notice of
protest, notice of intent to accelerate, notice of acceleration, dishonor,
diligence, notice of any amendment of the Loan Agreement, notice of any adverse
change in the financial condition of Borrower, notice of any adjustment,
indulgence, forbearance or compromise that might be granted or given by Bank to
Borrower, and also notice of acceptance of this Guaranty, acceptance on the
part of Bank being conclusively presumed by its request for this Guaranty and
delivery of the same to it.  The liability and obligations of Guarantor
hereunder shall not be affected or impaired by any action or inaction by Bank
in regard to any matter waived or notice of which is waived by Guarantor in
this paragraph or in any other paragraph of this Guaranty.

                 4.       Guarantor authorizes Bank, without notice or demand
and without affecting Guarantor's liability hereunder, (a) to take and hold
security for the payment of this Guaranty and/or the Guaranteed Indebtedness,
and to exchange, enforce, waive and/or release any such security; (b) to apply
such security and direct the order or manner of sale thereof as Bank in its
discretion may determine; (c) to obtain a guaranty of the Guaranteed
Indebtedness from any one or more other persons, corporations or entities
whomsoever and to enforce, waive, rearrange, modify, limit or release at any
time or times such other persons, corporations or entities from their
obligations under such guaranties; (d) to waive or delay the exercise of any of
its rights or remedies against the Borrower or any other person or entity; (e)
to renew, extend, or modify the terms of any of the Guaranteed Indebtedness or
any instrument or agreement evidencing the same; and (f) to fully or partially
release at any time any Guarantor which executes this Guaranty whether with or
without consideration.

                 5.       Guarantor waives any right to require Bank to (a)
proceed against, or make any effort at the collection of the Guaranteed
Indebtedness from Borrower or any other guarantor or party liable for the
Guaranteed Indebtedness; (b) proceed against or exhaust any collateral held by
Bank; or (c) pursue any other remedy in Bank's power whatsoever.  Guarantor
further waives any and all rights and remedies which Guarantor may have or be
able to assert by reason of the provisions of Chapter 34 of the Texas Business
and Commerce Code.  Guarantor waives any defense arising by reason of any
disability, lack of corporate authority or power, or other defense of Borrower
or any other guarantor of the Guaranteed Indebtedness, and Guarantor shall
remain liable under this Guaranty regardless of whether Borrower or any other
guarantor be found not liable on the Guaranteed Indebtedness for any reason
including, without limitation, insanity, minority, disability, bankruptcy,
insolvency, death or corporate dissolution, even though rendering the
Guaranteed Indebtedness void or unenforceable or uncollectible as against
Borrower or any other guarantor.  This Guaranty shall continue to be effective
or be reinstated, as the case may be, if at any time any payment of any of the
Guaranteed Indebtedness is rescinded or must otherwise be returned by Bank upon
the insolvency, bankruptcy or reorganization of Borrower or otherwise, all as
though such payment had not been made and will, thereupon, guarantee payment of
such amount as to which refund or restitution has been made, together with
interest accruing thereon subsequent to the





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date of refund or restitution at the applicable rate under the Loan Agreement
and collection costs and fees (including, without limitation, attorneys' fees)
applicable thereto, subject to the limitations set forth in Sections 1 and 10
hereof.

                 6.       The liability and obligations of Guarantor hereunder
shall not be affected or impaired by (a) the failure of Bank or any other party
to exercise diligence or reasonable care in the preservation, protection or
other handling or treatment of all or any part of the collateral securing
payment of all or any part of the Guaranteed Indebtedness, (b) the failure of
any security interest or lien intended to be granted or created to secure the
Guaranteed Indebtedness to be properly perfected or created or the
unenforceability of any security interest or lien for any other reason, or (c)
the subordination of any such security interest or lien to any other security
interest or lien.

                 7.       Bank may pursue any remedy without altering the
obligations of Guarantor hereunder and without liability to Guarantor, even
though Bank's pursuit of such remedy may result in Guarantor's loss of rights
of subrogation or to proceed against others for reimbursement or contribution
or any other right.  In no event shall any payment by Guarantor entitle it, by
subrogation or otherwise, to any rights against Borrower or any right to
participate in any security now or hereafter held by Bank prior to payment in
full of all of the Guaranteed Indebtedness and, in any event, not until 367
days after the making of any payment and/or the granting of any security
interest by Borrower or any other guarantor to Bank in connection with the
Guaranteed Indebtedness.

                 8.       Should the status of Borrower change in any way,
including, without limitation, as a result of any dissolution of Borrower, any
sale, lease or transfer of any or all of the assets of Borrower, any changes in
the shareholders of Borrower, or any reorganization of Borrower, this Guaranty
shall continue, and shall cover the Guaranteed Indebtedness under the new
status.

                 9.       The liability of Guarantor for the payment of the
Guaranteed Indebtedness shall be primary and not secondary.

                 10.      Guarantor is familiar with and has independently
reviewed the books and records regarding the financial condition of Borrower
and is familiar with the value of any and all collateral intended to be granted
as security for the payment of the Guaranteed Indebtedness; Guarantor is not,
however, relying on such financial condition or such collateral as an
inducement to enter into this Guaranty.  As of the date hereof, and after
giving effect to this Guaranty and the contingent obligations evidenced hereby,
Guarantor is, and will be, solvent, and has and will have assets and property
which, valued fairly, exceed such Guarantor's obligations, debts and
liabilities, and has and will have assets and property sufficient to satisfy,
repay and discharge the same.  Notwithstanding the definition of Guaranteed
Indebtedness herein, the liability of Guarantor hereunder is limited to (a) the
lowest amount that would render this Guaranty void against creditors or
creditors' representatives under any fraudulent conveyance or similar law or
under Sections 544 or 548 of the Bankruptcy Code of 1978, as revised, minus (b)
$1.00.





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                 11.      If Borrower shall at any time or times be or become
obligated to Bank for payment of any indebtedness other than the Guaranteed
Indebtedness, Bank (without in anywise impairing its rights hereunder or
diminishing Guarantor's liability) shall be at liberty at any time or times to
apply to such other indebtedness any amounts paid to or received by or coming
into the hands of Bank from or attributable to Borrower or any other person or
party liable for any of such other indebtedness or from or attributable to or
representing proceeds of any property or security held by Bank securing payment
of such other indebtedness or any credits, deposits or offsets due Borrower or
other party liable on any of such other indebtedness (whether or not the
Guaranteed Indebtedness or such other indebtedness are then due), it being
intended to give Bank the right to apply all payments, credits and offsets and
amounts becoming available for application on or credit against the
indebtedness of Borrower to Bank (now or hereafter existing) first toward
payment and satisfaction of the Borrower's indebtedness not hereby guaranteed,
before making application thereof on or against the Guaranteed Indebtedness.

                 12.      Guarantor represents and warrants that this Guaranty
accurately and completely embodies the entire agreement between Guarantor and
Bank with respect to the respective rights, obligations and liabilities of
Guarantor and Bank hereunder, and supersedes all prior agreements and
understandings, if any, relating to the subject matter hereof.  Guarantor
acknowledges that Guarantor is not relying on any representations (oral or
otherwise) of Bank, or any other party, other than as expressly described in
this Guaranty.

                 13.      This Guaranty was reviewed by Guarantor, and
Guarantor acknowledges and agrees that Guarantor (a) understands fully all of
the terms of this Guaranty and the consequences and implications of Guarantor's
execution of this Guaranty, and (b) has been afforded an opportunity to have
this Guaranty reviewed by, and to discuss the terms, consequences and
implications of this Guaranty with an attorney or other such persons as
Guarantor may have desired.

                 14.      This Guaranty is and shall be in every particular
available to the successors and assigns of Bank and is and shall always be
fully binding upon the heirs, executors, administrators, successors and assigns
of Guarantor.  This Guaranty is intended for and shall inure to the benefit of
Bank and each and every other person who shall from time to time be or become
the owner or holder of any of the Guaranteed Indebtedness, and each and every
reference herein to "Bank" shall also include and refer to each and every
successor or assignee of Bank at any time holding or owning any part of or
interest in any part of the Guaranteed Indebtedness.  This Guaranty shall be
transferable and negotiable, with the same force and effect and to the same
extent that the Guaranteed Indebtedness is transferable, it being understood
and stipulated that upon the assignment or transfer by Bank of any of the
Guaranteed Indebtedness the legal or beneficial owner of the Guaranteed
Indebtedness (or part thereof or interest therein thus transferred or assigned
by Bank) shall also, unless provided otherwise by Bank in its assignment, have
and may exercise all of the rights granted to Bank under this Guaranty to the
extent of the part of or interest in the Guaranteed Indebtedness thus assigned
or transferred to such person or entity.  Guarantor expressly waives notice of
transfer or assignment of the Guaranteed Indebtedness, or any part thereof, or
of the rights of Bank hereunder.





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                 15.      All amounts becoming payable by Guarantor to Bank
under this Guaranty shall be payable at Bank's offices in the City of Houston,
Harris County, Texas.

                 16.      Any notice hereunder to Guarantor shall be in
writing, duly stamped and addressed to Guarantor at the address shown below
Guarantor's signature hereto, or at such other address as Guarantor may by
written notice, received by Bank, have designated as Guarantor's address for
such purpose.  Any notice provided for herein shall become effective upon the
earlier of (a) the first business day of Bank following the deposit in a
regularly maintained postal deposit box of the United States Postal Service, or
(b) the day of its receipt by Guarantor; but actual notice, however given or
received, shall always be effective.  The preceding sentence shall not be
construed in anywise to affect or impair any waiver of notice or demand herein
provided or to require giving of notice or demand to or upon Guarantor in any
situation or for any reason.

                 17.      It is the intention of the parties hereto to comply
strictly with all applicable usury laws; accordingly, it is agreed that
notwithstanding any provisions to the contrary in this Guaranty, or in any
documents securing payment hereof or otherwise relating hereto, in no event
shall this Guaranty or such documents require the payment or permit the
collection of an aggregate amount of interest in excess of the maximum amount
permitted by such laws, including the laws of the State of Texas and the laws
of the United States of America.  If any such excess of interest is contracted
for, charged or received under this Guaranty or under the terms of any
documents securing payment hereof or otherwise relating hereto, or if under any
circumstances, the amount of interest (including all amounts payable hereunder
which are not denominated as interest but which constitute interest under the
applicable laws) contracted for, charged or received under this Guaranty shall
exceed the maximum amount of interest permitted by the applicable usury laws,
then in any such event (a) the provisions of this paragraph shall govern and
control, (b) Guarantor shall not be obligated to pay the amount of such
interest to the extent that it is in excess of the maximum amount of interest
permitted by the applicable usury laws, (c) any such excess interest which may
have been collected shall be either applied as a credit against the then unpaid
Guaranteed Indebtedness or, if the Guaranteed Indebtedness shall have been paid
in full, refunded to Guarantor, and (d) the effective rate of interest shall be
automatically reduced to the maximum lawful contract rate allowed under the
applicable usury laws as now or hereafter construed by the courts having
jurisdiction thereof.  It is further agreed that without limitation of the
foregoing, all calculations of the rate of interest contracted for, charged or
received under this Guaranty or under such other documents which are made for
the purpose of determining whether such rate exceeds the maximum lawful
contract rate, shall be made, to the extent permitted by applicable usury laws,
by amortizing, prorating, allocating and spreading in equal parts during the
full period during which this Guaranty is to be in effect, all interest at any
time contracted for, charged or received from Guarantor or otherwise by the
holder or holders hereof in connection with this Guaranty.

                 18.      In case any of the provisions of this Guaranty shall
for any reason be held to be invalid, illegal, or unenforceable, such
invalidity, illegality, or unenforceability shall not affect





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any other provisions hereof, and this Guaranty shall be construed as if such
invalid, illegal, or unenforceable provision had never been contained herein.

                 19.      In all instances herein, the singular shall be
construed to include the plural and the masculine to include the feminine.

                 20.      This Guaranty may be executed in multiple
counterparts each of which shall constitute an original, but all of which when
taken together shall constitute one and the same Guaranty.

                 21.      THIS GUARANTY SHALL BE GOVERNED BY AND CONSTRUED IN
ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS AND THE UNITED STATES OF
AMERICA.  All actions or proceedings with respect to the Guaranteed
Indebtedness or this Guaranty may be instituted in the Courts of the State of
Texas located in Harris County, Texas, or the United States District Court for
the Southern District of Texas, and by execution and delivery of this Guaranty,
Guarantor irrevocably and unconditionally submits to the jurisdiction (both
subject matter and personal) of each such Court, and irrevocably and
unconditionally waives (a) any objection Guarantor may now or hereafter have to
the laying of venue in any such Courts, (b) any claim that any action or
proceeding brought in any of such Courts has been brought in an inconvenient
forum, and (c) any right to bring any action or proceeding with respect to the
Guaranteed Indebtedness or this Guaranty in any forum other than the courts of
the State of Texas located in Harris County, Texas, or the United States
District Court for the Southern District of Texas.

                 22.      Guarantor represents and warrants to Bank that this
Guaranty is a valid, binding and enforceable obligation of Guarantor and does
not violate any provisions of any law, rule, regulation, contract or agreement
enforceable against Guarantor.

                 23.      Guarantor hereby agrees that a counterpart of this
Guaranty bearing the signature of Guarantor may be effectively delivered to the
Bank by the delivery of an electronic facsimile sent via telecopier; and that
Guarantor shall be bound by his facsimile signature thereon.

                 EXECUTED this 24th day of September, 1998.

                                       GUARANTOR:
                                       
                                       
                                       
                                       ----------------------------------------
                                       DOUGLAS A. P. HAMILTON
                                       
                                       Address:    c/o Anatar Investments, Inc.
                                                   45 Rockefeller Plaza
                                                   20th Floor
                                                   New York, NY 10111




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STATE OF NEW YORK

COUNTY OF NEW YORK



                 We, ___________________________ and _________________________,
sign our names to this instrument as witnesses to the signature of DOUGLAS A. P.
HAMILTON (the "Signor"), and being duly sworn, do hereby declare to the
undersigned authority that we are personally acquainted with the Signor, that
we know the Signor to be the person that he purports to be through his
signature, that he has signed this instrument willingly, and that each of us,
in the presence and hearing of the Signor, the undersigned authority, and each
other, hereby execute this instrument as witnesses to the Signor's signing, and
that to the best of our knowledge, the Signor is twenty-one years of age or
older, of sound mind, and under no constraint or undue influence.


                                       WITNESSES:
                                       
                                       
                                                                          
                                       -----------------------------------
                                       Printed Name:
                                       
                                       
                                                                          
                                       -----------------------------------
                                       Printed Name:


STATE OF NEW YORK

COUNTY OF NEW YORK


                 The foregoing instrument was subscribed, sworn to and
acknowledged before me by DOUGLAS A. P. HAMILTON the Signor, and was also
subscribed and sworn to before me by _________________________and _______
__________________, as witnesses, this ______ day of September, 1996.


                                       
                                       ------------------------
                                       Notary Public in and for
                                       The State of                       
                                                    -----------


[Notarial Seal or Stamp]





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