Exhibit 10.1

VOTING AGREEMENT

BY AND AMONG

DUNCAN ENERGY PARTNERS L.P.

AND

ENTERPRISE PRODUCTS PARTNERS L.P.

AND

ENTERPRISE GTM HOLDINGS L.P.

DATED AS OF APRIL 28, 2011

VOTING AGREEMENT

     VOTING AGREEMENT, dated as of April 28, 2011 (this “Agreement”), by and among Duncan Energy Partners L.P. (“Duncan”), a Delaware limited partnership, Enterprise Products Partners L.P., a Delaware limited partnership (the “Partnership”) and Enterprise GTM Holdings L.P., a Delaware limited partnership (the “Unitholder” and, together with the Partnership, the “Partnership Parties” and each a “Partnership Party”) .

WITNESSETH:

     Whereas, concurrently with the execution of this Agreement, the Partnership, Enterprise Products Holdings LLC, a Delaware limited liability company and the general partner of the Partnership (the “General Partner”), EPD MergerCo LLC, a Delaware limited liability company and wholly owned subsidiary of the Partnership (“MergerCo”), Duncan and DEP Holdings, LLC, a Delaware limited liability company and the general partner of Duncan (“Duncan GP”) are entering into an Agreement and Plan of Merger, dated as of the date hereof (as amended, supplemented, restated or otherwise modified from time to time, the “Merger Agreement”) pursuant to which, among other things, MergerCo will merge with and into Duncan (the “Merger”), with Duncan as the surviving entity, and each outstanding common unit representing limited partner interests of Duncan (collectively, the “Units” and, individually, a “Unit”) will be converted into the right to receive the merger consideration specified therein; and

     Whereas, the Unitholder is an indirect wholly owned subsidiary of the Partnership and, as of the date hereof, is the record or direct owner in the aggregate of, and has the right to vote and dispose of, 33,783,587 Units (the “Existing Units”); and

     Whereas, in connection with the Merger, Duncan has requested that each of the Partnership Parties enter into this Agreement and abide by the covenants and obligations with respect to the Covered Units (as hereinafter defined), set forth herein; and

     Now Therefore, in consideration of the foregoing and the mutual representations, warranties, covenants and agreements herein contained, and intending to be legally bound hereby, the parties hereto agree as follows:

ARTICLE 1

GENERAL

     1.1 Defined Terms. The following capitalized terms, as used in this Agreement, shall have the meanings set forth below. Capitalized terms used but not otherwise defined herein shall have the meanings ascribed thereto in the Merger Agreement.

     “Acquisition Proposal” has the meaning set forth in the Merger Agreement.

     “Business Day” has the meaning set forth in the Merger Agreement.

     “Covered Units” means the Unitholder’s Existing Units together with any Units that the Unitholder, the Partnership or any of their Subsidiaries acquires of record on or after the date hereof.

     “Duncan Audit Committee” has the meaning set forth in the Merger Agreement.

     “Duncan Change in Recommendation” has the meaning set forth in the Merger Agreement.

     “Duncan Partnership Agreement” means the Amended and Restated Agreement of Limited Partnership of Duncan, dated effective as of February 5, 2007, as amended to date.

     “Effective Time” has the meaning set forth in the Merger Agreement.

     “Exchange Act” means the Securities Exchange Act of 1934, as amended, and the rules and regulations thereunder.

     “Grantee” or “Grantees” has the meaning set forth in Section 2.3 of this Agreement.

     “Lien” means any mortgage, lien, charge, restriction (including restrictions on transfer), pledge, security interest, option, right of first offer or refusal, preemptive right, put or call option, lease or sublease, claim, right of any third party, covenant, right of way, easement, encroachment or encumbrance.

     “Order” or “Orders” has the meaning set forth in Section 3.1(c) of this Agreement.

     “Person” means any individual, corporation, limited liability company, limited or general partnership, joint venture, association, joint stock company, trust, unincorporated organization, government or any agency or political subdivision thereof or any other entity, or any group comprised of two or more of the foregoing.

     “Proxy Statement/Prospectus” has the meaning set forth in the Merger Agreement.

     “Representative” or “Representatives” has the meaning set forth in the Merger Agreement.

     “Subsidiary” or “Subsidiaries” has the meaning set forth in the Merger Agreement.

     “Transfer” means, directly or indirectly, to sell, transfer, assign or similarly dispose of (by merger (including by conversion into securities or other consideration), by tendering into any tender or exchange offer, by testamentary disposition, by operation of law or otherwise), either voluntarily or involuntarily, or to enter into any contract, option or other arrangement or understanding with respect to the voting of or sale, transfer, assignment or similar disposition of (by merger (including by conversion into securities or other consideration), by tendering into any tender or exchange offer, by testamentary disposition, by operation of law or otherwise); provided that, for purposes of clarification, a Transfer shall not include any existing or future pledges or security interests issued by either of the Partnership Parties in connection with a bona fide loan.

ARTICLE 2

VOTING

     2.1 Agreement to Vote Covered Units and Member Interests. Each of the Partnership Parties hereby irrevocably and unconditionally agrees that during the term of this Agreement, at any meeting of the unitholders of Duncan, however called, including any adjournment or postponement thereof, and in connection with any written consent of the unitholders of Duncan, it shall, to the fullest extent that the Covered Units are entitled to vote thereon or consent thereto:

          (a) appear at each such meeting or otherwise cause its Covered Units to be counted as present thereat for purposes of calculating a quorum; and

          (b) vote (or cause to be voted), in person or by proxy, or deliver (or cause to be delivered) a written consent covering, all of the Covered Units (i) in favor of the adoption of the Merger Agreement, any transactions contemplated by the Merger Agreement and any other action reasonably requested by Duncan in furtherance thereof, submitted for the vote or written consent of the unitholders of Duncan; (ii) against any action or agreement that would result in a breach of any covenant, representation or warranty or any other obligation or agreement of Duncan or Duncan GP or any of their Subsidiaries contained in the Merger Agreement; and (iii) against any action, agreement or transaction that would impede, interfere with, delay, postpone, discourage, frustrate the purposes of or adversely affect the Merger or the other transactions contemplated by the Merger Agreement.

     2.2 No Inconsistent Agreements. Each of the Partnership Parties hereby represents, covenants and agrees that, except for this Agreement, it (a) has not entered into, and shall not enter into at any time while this Agreement remains in effect, any voting agreement or voting trust with respect to its Covered Units, (b) has not granted, and shall not grant at any time while this Agreement remains in effect, a proxy, consent or power of attorney with respect to its Covered Units (except pursuant to Section 2.3 hereof) and (c) has not taken and shall not knowingly take any action that would make any representation or warranty of such Partnership Party contained herein untrue or incorrect or have the effect of preventing or disabling such Partnership Party from performing any of its obligations under this Agreement.

     2.3 Proxy. In order to secure the obligations set forth herein, each of the Partnership Parties hereby irrevocably appoints as its proxy and attorney-in-fact, as the case may be, W. Randall Fowler and Stephanie C. Hildebrandt, in their respective capacities as officers of Duncan GP, and any individual who shall hereafter succeed to any such officer of Duncan GP, as the case may be, and any other Person designated in writing by Duncan GP (collectively, the “Grantees”), each of them individually, with full power of substitution, to vote or execute written consents with respect to the Covered Units in accordance with Section 2.1 hereof and, in the discretion of the Grantees, with respect to any proposed postponements or adjournments of any meeting of the unitholders of Duncan at which any of the matters described in Section 2.1 are to be considered. This proxy is coupled with an interest and shall be irrevocable, except upon termination of this Agreement, and each of the Partnership Parties will take such further action or execute such other instruments as may be necessary to effectuate the intent of this

proxy and hereby revokes any proxy previously granted by it with respect to the Covered Units. Duncan may terminate this proxy with respect to the Partnership Parties at any time at its sole election by written notice provided to the Partnership Parties.

ARTICLE 3

REPRESENTATIONS AND WARRANTIES

     3.1 Representations and Warranties of the Partnership Parties. Each of the Partnership Parties (except to the extent otherwise provided herein) hereby severally but not jointly represents and warrants to Duncan as follows:

          (a) Organization; Authorization; Validity of Agreement; Necessary Action. Each of the Partnership Parties has the requisite power and authority and/or capacity to execute and deliver this Agreement, to carry out its obligations hereunder and to consummate the transactions contemplated hereby. The execution and delivery by such Partnership Party of this Agreement, the performance by it of the obligations hereunder and the consummation of the transactions contemplated hereby have been duly and validly authorized by such Partnership Party and no other actions or proceedings on the part of such Partnership Party to authorize the execution and delivery of this Agreement, the performance by it of the obligations hereunder or the consummation of the transactions contemplated hereby are required. This Agreement has been duly executed and delivered by each of the Partnership Parties and, assuming the due authorization, execution and delivery of this Agreement by Duncan, constitutes a legal, valid and binding agreement of each of the Partnership Parties, enforceable against it in accordance with its terms, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equitable principles.

          (b) Ownership. The Unitholder legally owns the Unitholder’s Existing Units, and all of the Covered Units owned by either of the Partnership Parties or their Subsidiaries from the date hereof through and on the Closing Date will be beneficially or legally owned by such Partnership Party. The Unitholder’s Existing Units are all of the Units legally or beneficially owned by the Unitholder. The Unitholder has and will have at all times through the Closing Date sole voting power (including the right to control such vote as contemplated herein), sole power of disposition, sole power to issue instructions with respect to the matters set forth in Article 2 hereof, and sole power to agree to all of the matters set forth in this Agreement, in each case with respect to all of the Unitholder’s Existing Units and with respect to all of the Covered Units owned by the Unitholder at all times through the Closing Date. The Partnership Parties or any of their Subsidiaries who acquire any Covered Units will have sole voting power (including the right to control such vote as contemplated herein), sole power of disposition, sole power to issue instructions with respect to the matters set forth in Article 2 hereof, and sole voting power to agree to all of the matters set forth in this Agreement, with respect to all of the Covered Units owned by such entity at all times through the Closing Date.

          (c) No Violation. Neither the execution and delivery of this Agreement by either of the Partnership Parties nor the performance by it of its obligations under this

Agreement will (i) result in a violation or breach of or conflict with any provisions of, or constitute a default (or an event which, with notice or lapse of time or both, would constitute a default) under, or result in the termination, cancellation of, or give rise to a right of purchase under, or accelerate the performance required by, or result in a right of termination or acceleration under, or result in the creation of any Lien upon any of the properties, rights or assets, including the Existing Units, owned by such Partnership Party, or result in being declared void, voidable, or without further binding effect, or otherwise result in a detriment to it under any of the terms, conditions or provisions of any note, bond, mortgage, indenture, deed of trust, license, contract, lease, agreement or other instrument or obligation of any kind to which such Partnership Party is a party or by which it or any of its respective properties, rights or assets may be bound, (ii) violate any judgments, decrees, injunctions, rulings, awards, settlements, stipulations or orders (collectively, “Orders”) or laws applicable to such Partnership Party or any of its properties, rights or assets or (iii) result in a violation or breach of or conflict with its organizational and governing documents.

          (d) Consents and Approvals. No consent, approval, Order or authorization of, or registration, declaration or filing with, any governmental authority is necessary to be obtained or made by either of the Partnership Parties in connection with such Partnership Party’s execution, delivery and performance of this Agreement or the consummation by such Partnership Party of the transactions contemplated hereby, except for any reports under Sections 13(d) and 16 of the Exchange Act as may be required in connection with this Agreement and the transactions contemplated hereby.

          (e) Reliance by Duncan. Each of the Partnership Parties understands and acknowledges that Duncan is entering into the Merger Agreement in reliance upon the execution and delivery of this Agreement and the representations, warranties, covenants and obligations of such Partnership Party contained herein.

     3.2 Representations and Warranties of Duncan. Duncan hereby represents and warrants to each of the Partnership Parties that the execution and delivery of this Agreement by Duncan and the consummation of the transactions contemplated hereby have been duly authorized by all necessary action on the part of Duncan GP.

ARTICLE 4

OTHER COVENANTS

     4.1 Prohibition on Transfers, Other Actions. Each of the Partnership Parties hereby agrees not to (a) Transfer any of the Covered Units, beneficial ownership thereof or any other interest therein; (b) enter into any agreement, arrangement or understanding, or take any other action, that violates or conflicts with or would reasonably be expected to violate or conflict with, or result in or give rise to a violation of or conflict with, such Partnership Party’s representations, warranties, covenants and obligations under this Agreement; or (c) take any action that could restrict or otherwise affect such Partnership Party’s legal power, authority and right to comply with and perform its covenants and obligations under this Agreement; provided, the foregoing shall not include or prohibit Transfers resulting from pledges or security interests (or the foreclosure thereof) relating to existing or future bona fide loans that do not affect such

Partnership Party’s legal power, authority and right to comply with and perform its covenants and obligations under this Agreement. Any Transfer in violation of this provision shall be null and void.

     4.2 Unit Splits and Unit Distributions. In the event of a unit split, unit distribution or any change in the Units by reason of any split-up, reverse unit split, recapitalization, combination, reclassification, exchange of units or the like, the terms “Covered Units” and “Existing Units” shall be deemed to refer to an include such Units as well as all such distributions and any securities of Duncan into which or for which any or all of such Units may be changed or exchanged or which are received in such transaction.

     4.3 Further Assurances. From time to time, at Duncan’s request and without further consideration, each of the Partnership Parties shall execute and deliver such additional documents and take all such further action as may be reasonably necessary or advisable to effect the actions and consummate the transactions contemplated by this Agreement.

ARTICLE 5

MISCELLANEOUS

     5.1 Termination. This Agreement shall remain in effect until the earliest to occur of (a) the Effective Time, (b) the termination of the Merger Agreement in accordance with its terms (including after any extension thereof) and (c) the written agreement of the Unitholder, the Partnership and Duncan to terminate this Agreement. After the occurrence of such applicable event, this Agreement shall terminate and be of no further force or effect. Nothing in this Section 5.1 and no termination of this Agreement shall relieve or otherwise limit any party of liability for any breach of this Agreement occurring prior to such termination.

     5.2 No Ownership Interest. Nothing contained in this Agreement shall be deemed to vest in Duncan any direct or indirect ownership or incidence of ownership of or with respect to any Covered Units. All rights, ownership and economic benefit relating to the Covered Units shall remain vested in and belong to the Partnership Parties, and Duncan shall have no authority to direct the Partnership Parties in the voting or disposition of any of the Covered Units, except as otherwise provided herein.

     5.3 Publicity. The Unitholder hereby permits the Partnership and Duncan to include and disclose in the Proxy Statement/Prospectus and in such other schedules, certificates, applications, agreements or documents as such entities reasonably determine to be necessary or appropriate in connection with the consummation of the Merger and the transactions contemplated by the Merger Agreement the Unitholder’s identity and ownership of the Covered Units and the nature of the Unitholder’s commitments, arrangements and understandings pursuant to this Agreement.

     5.4 Notices. All notices and other communications hereunder shall be in writing and shall be deemed given when delivered personally or by telecopy (upon telephonic confirmation of receipt) or on the first Business Day following the date of dispatch if delivered by a recognized next day courier service. All notices hereunder shall be delivered as set forth below

or pursuant to such other instructions as may be designated in writing by the party to receive such notice:

     If to the Unitholder or the Partnership, to:

Enterprise GTM Holdings L.P.
Enterprise Products Partners L.P.
1100 Louisiana, 10th Floor
Houston, Texas 77002
Attention: President and Chief Executive Officer

     With copies to:

Andrews Kurth LLP
600 Travis, Suite 4200
Houston, Texas 77002
Attention: David C. Buck, Esq.

     If to Duncan, to:

Duncan Energy Partners L.P.
1100 Louisiana, 10th Floor
Houston, Texas 77002
Attention: President and Chief Executive Officer

     With copies to:

Baker & Hostetler LLP
1000 Louisiana, Suite 2000
Houston, Texas 77002
Attention: Donald W. Brodsky, Esq.

and

Vinson & Elkins L.L.P.
1001 Fannin, Suite 2500
Houston, Texas 77002
Attention: Douglas E. McWilliams, Esq.

     5.5 Interpretation. The words “hereof,” “herein” and “hereunder” and words of similar import when used in this Agreement shall refer to this Agreement as a whole and not to any particular provision of this Agreement, and Section references are to this Agreement unless otherwise specified. Whenever the words “include,” “includes” or “including” are used in this Agreement, they shall be deemed to be followed by the words “without limitation.” The meanings given to terms defined herein shall be equally applicable to both the singular and plural forms of such terms. The headings contained in this Agreement are for reference purposes only

and shall not affect in any way the meaning or interpretation of this Agreement. This Agreement is the product of negotiation by the parties having the assistance of counsel and other advisers. It is the intention of the parties that this Agreement not be construed more strictly with regard to one party than with regard to the others.

     5.6 Counterparts. This Agreement may be executed by facsimile and in counterparts, all of which shall be considered one and the same agreement and shall become effective when counterparts have been signed by each of the parties and delivered to the other parties, it being understood that all parties need not sign the same counterpart.

     5.7 Entire Agreement. This Agreement and, solely to the extent of the defined terms referenced herein, the Merger Agreement, together with the schedules annexed hereto, embody the complete agreement and understanding among the parties hereto with respect to the subject matter hereof and supersede and preempt any prior understandings, agreements or representations by or among the parties, written and oral, that may have related to the subject matter hereof in any way.

     5.8 Governing Law; Consent to Jurisdiction; Waiver of Jury Trial.

          (a) This Agreement shall be governed by and construed in accordance with the laws of the State of Delaware, regardless of the laws that might otherwise govern under applicable principles of conflicts of laws thereof.

          (b) Each of the parties hereto (i) consents to submit itself to the personal jurisdiction of the Court of Chancery of the State of Delaware (and any appellate court of the State of Delaware) and the Federal courts of the United States of America located in the State of Delaware in the event any dispute arises out of this Agreement or the transactions contemplated by this Agreement, (ii) agrees that it will not attempt to deny or defeat such personal jurisdiction by motion or other request for leave from any such court and (iii) agrees that it will not bring any action relating to this Agreement or the transactions contemplated by this Agreement in any court other than the Court of Chancery of the State of Delaware or a Federal court of the United States of America located in the State of Delaware. Without limiting the foregoing, each party agrees that service of process on such party as provided in Section 5.4 shall be deemed effective service of process on such party.

          (c) EACH PARTY HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES ANY RIGHT IT MAY HAVE TO A TRIAL BY JURY IN RESPECT OF ANY LITIGATION DIRECTLY OR INDIRECTLY ARISING OUT OF OR RELATING TO THIS AGREEMENT AND ANY OF THE AGREEMENTS DELIVERED IN CONNECTION HEREWITH OR THE TRANSACTIONS CONTEMPLATED HEREBY OR THEREBY. EACH PARTY CERTIFIES AND ACKNOWLEDGES THAT (I) NO REPRESENTATIVE, AGENT OR ATTORNEY OF ANY OTHER PARTY HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE EITHER OF SUCH WAIVERS, (II) IT UNDERSTANDS AND HAS CONSIDERED THE IMPLICATIONS OF SUCH WAIVERS, (III) IT MAKES SUCH WAIVERS VOLUNTARILY, AND (IV) IT HAS

BEEN INDUCED TO ENTER INTO THIS AGREEMENT BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS IN THIS SECTION 5.8.

     5.9 Amendment; Waiver. This Agreement may not be amended except by an instrument in writing signed by Duncan, the Partnership and the Unitholder. Each party may waive any right of such party hereunder by an instrument in writing signed by such party and delivered to the other parties hereto.

     5.10 Remedies.

          (a) Each party hereto acknowledges that monetary damages would not be an adequate remedy in the event that any covenant or agreement in this Agreement is not performed in accordance with its terms, and it is therefore agreed that, in addition to and without limiting any other remedy or right it may have, the non-breaching party will have the right to an injunction, temporary restraining order or other equitable relief in any court of competent jurisdiction enjoining any such breach and enforcing specifically the terms and provisions hereof. Each party hereto agrees not to oppose the granting of such relief in the event a court determines that such a breach has occurred, and to waive any requirement for the securing or posting of any bond in connection with such remedy.

          (b) All rights, powers and remedies provided under this Agreement or otherwise available in respect hereof at law or in equity shall be cumulative and not alternative, and the exercise or beginning of the exercise of any thereof by any party shall not preclude the simultaneous or later exercise of any other such right, power or remedy by such party.

     5.11 Severability. Any term or provision of this Agreement which is determined by a court of competent jurisdiction to be invalid or unenforceable in any jurisdiction shall, as to that jurisdiction, be ineffective to the extent of such invalidity or unenforceability without rendering invalid or unenforceable the remaining terms and provisions of this Agreement or affecting the validity or enforceability of any of the terms or provisions of this Agreement in any other jurisdiction, and if any provision of this Agreement is determined to be so broad as to be unenforceable, the provision shall be interpreted to be only so broad as is enforceable, in all cases so long as neither the economic nor legal substance of the transactions contemplated hereby is affected in any manner adverse to any party or its equityholders. Upon any such determination, the parties shall negotiate in good faith in an effort to agree upon a suitable and equitable substitute provision to effect the original intent of the parties as closely as possible and to the end that the transactions contemplated hereby shall be fulfilled to the maximum extent possible.

     5.12 Action by Duncan. No waiver, consent or other action by or on behalf of Duncan pursuant to or as contemplated by this Agreement shall have any effect unless such waiver, consent or other action is expressly approved by the Board of Directors of Duncan GP and the Duncan Audit Committee.

     5.13 Successors and Assigns; Third Party Beneficiaries. Neither this Agreement nor any of the rights or obligations of any party under this Agreement shall be assigned, in whole

or in part (by operation of law or otherwise), by any party without the prior written consent of the other parties hereto. Subject to the foregoing, this Agreement shall bind and inure to the benefit of and be enforceable by the parties hereto and their respective successors and permitted assigns. Nothing in this Agreement, express or implied, is intended to confer on any Person other than the parties hereto or the parties’ respective successors and permitted assigns any rights, remedies, obligations or liabilities under or by reason of this Agreement.

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     In Witness Whereof, the parties hereto have caused this Agreement to be signed (where applicable, by their respective officers or other authorized Person thereunto duly authorized) as of the date first written above.

Signature Page to Voting Agreement