INVESTMENT SUB-ADVISORY AGREEMENT

      AGREEMENT made as of this 8th day of January, 2008 by and
among Energy Income and Growth Fund, a Massachusetts business
trust (the "Fund"), First Trust Advisors L.P., an Illinois
limited partnership and a registered investment adviser with the
Securities and Exchange Commission ("SEC") (the "Manager"), and
Energy Income Partners, LLC, a Delaware limited liability company
and a registered investment adviser with the SEC (the "Sub-
Adviser").

      WHEREAS, the Fund is a closed-end management investment
company registered under the Investment Company Act of 1940, as
amended (the "1940 Act");

      WHEREAS, the Fund has retained the Manager to serve as the
investment manager for the Fund pursuant to an Investment
Management Agreement between the Manager and the Fund (as such
agreement may be modified from time to time, the "Management
Agreement");

      WHEREAS, the Management Agreement provides that the Manager
may, subject to the initial and periodic approvals required under
Section 15 of the 1940 Act, appoint a sub-adviser at its own cost
and expense for the purpose of furnishing certain services
required under the Management Agreement;

      WHEREAS, the Fund and the Manager desire to retain the Sub-
Adviser to furnish investment advisory services for the Fund's
investment portfolio, upon the terms and conditions hereafter set
forth;

      NOW, THEREFORE, in consideration of the mutual covenants
herein contained, the parties hereto agree as follows:

	1.	Appointment.  The Fund and the Manager hereby appoint
the Sub-Adviser to provide certain sub-investment advisory
services to the Fund for the period and on the terms set forth in
this Agreement.  The Sub-Adviser accepts such appointment and
agrees to furnish the services herein set forth for the
compensation herein provided.  The Sub-Adviser shall, for all
purposes herein provided, be deemed an independent contractor
and, unless otherwise expressly provided or authorized, shall
have no authority to act for nor represent the Fund or Manager in
any way, nor otherwise be deemed an agent of the Fund or the
Manager.

	2.	Services to Be Performed.  Subject always to the
supervision of the Fund's Board of Trustees and the Manager, the
Sub-Adviser will act as sub-adviser for, and manage on a
discretionary basis the investment and reinvestment of the assets
of the Fund, furnish an investment program in respect of, make
investment decisions for, and place all orders for the purchase
and sale of securities for the Fund's investment portfolio, all
on behalf of the Fund and as described in the Fund's most recent
effective registration statement on Form N-2 as declared
effective by the SEC, and as the same may thereafter be amended
from time to time.  In the performance of its duties, the Sub-
Adviser will in all material respects (a) satisfy any applicable
fiduciary duties it may have to the Fund, (b) monitor the Fund's
investments, and (c) comply with the provisions of the Fund's
Declaration of Trust and By-laws, as amended from time to time
and communicated by the Fund or the Manager to the Sub-Adviser in
writing, and the stated investment objectives, policies and
restrictions of the Fund as such objectives, policies and
restrictions may subsequently be changed by the Fund's Board of
Trustees and communicated by the Fund or the Manager to the
Sub-Adviser in writing.  The Fund or the Manager has provided the
Sub-Adviser with current copies of the Fund's Declaration of
Trust, By-laws, prospectus, statement of additional information
and any amendments thereto, and any objectives, policies or
limitations not appearing therein as they may be relevant to the
Sub-Adviser's performance under this Agreement.

      The Sub-Adviser is authorized to select the brokers or
dealers that will execute the purchases and sales of portfolio
investments for the Fund, and is directed to use its commercially
reasonable efforts to obtain best execution, which includes most
favorable net results and execution of the Fund's orders, taking
into account all appropriate factors, including price, dealer
spread or commission, size and difficulty of the transaction and
research or other services provided.  Subject to approval by the
Fund's Board of Trustees and compliance with the policies and
procedures adopted by the Board of Trustees for the Fund and to
the extent permitted by and in conformance with applicable law
(including Rule 17e-1 of the 1940 Act), the Sub-Adviser may
select brokers or dealers affiliated with the Sub-Adviser.  It is
understood that the Sub-Adviser will not be deemed to have acted
unlawfully, or to have breached a fiduciary duty to the Fund, or
be in breach of any obligation owing to the Fund under this
Agreement, or otherwise, solely by reason of its having caused
the Fund to pay a member of a securities exchange, a broker or a
dealer a commission for effecting a securities transaction for
the Fund in excess of the amount of commission another member of
an exchange, broker or dealer would have charged if the Sub-
Adviser determined in good faith that the commission paid was
reasonable in relation to the brokerage or research services
provided by such member, broker or dealer, viewed in terms of
that particular transaction or the Sub-Adviser's overall
responsibilities with respect to its accounts, including the
Fund, as to which it exercises investment discretion.

      In addition, the Sub-Adviser may, to the extent permitted by
applicable law, aggregate purchase and sale orders of securities
placed with respect to the assets of the Fund with similar orders
being made simultaneously for other accounts managed by the Sub-
Adviser or its affiliates, if in the Sub-Adviser's reasonable
judgment such aggregation shall result in an overall economic
benefit to the Fund, taking into consideration the selling or
purchase price, brokerage commissions and other expenses.  In the
event that a purchase or sale of an asset of the Fund occurs as
part of any aggregate sale or purchase orders, the objective of
the Sub-Adviser and any of its affiliates involved in such
transaction shall be to allocate the securities so purchased or
sold, as well as expenses incurred in the transaction, among the
Fund and other accounts in a fair and equitable manner.
Nevertheless, the Fund and the Manager acknowledge that under
some circumstances, such allocation may adversely affect the Fund
with respect to the price or size of the securities positions
obtainable or salable.  Whenever the Fund and one or more other
investment advisory clients of the Sub-Adviser have available
funds for investment, investments suitable and appropriate for
each will be allocated in a manner believed by the Sub-Adviser to
be equitable to each, although such allocation may result in a
delay in one or more client accounts being fully invested that
would not occur if such an allocation were not made.  Moreover,
it is possible that due to differing investment objectives or for
other reasons, the Sub-Adviser and its affiliates may purchase
securities or loans of an issuer for one client and at
approximately the same time recommend selling or sell the same or
similar types of securities or loans for another client.

      The Sub-Adviser will not arrange purchases or sales of
securities between the Fund and other accounts advised by the
Sub-Adviser or its affiliates unless (a) such purchases or sales
are in accordance with applicable law (including Rule 17a-7 of
the 1940 Act) and the Fund's policies and procedures, (b) the
Sub-Adviser determines the purchase or sale is in the best
interests of the Fund, and (c) the Fund's Board of Trustees has
approved these types of transactions.

      The Fund may adopt policies and procedures that modify or
restrict the Sub-Adviser's authority regarding the execution of
the Fund's portfolio transactions provided herein.  Such policies
and procedures and any amendments thereto will be communicated by
the Manager to the Sub-Adviser.

      The Sub-Adviser will communicate to the officers and
Trustees of the Fund such information relating to transactions
for the Fund as they may reasonably request.  In no instance will
the Fund's portfolio securities be purchased from or sold to the
Manager, the Sub-Adviser or any affiliated person of either the
Fund, the Manager, or the Sub-Adviser, except as may be permitted
under the 1940 Act.

      The Sub-Adviser further agrees that it:

	(a)	will use the same degree of skill and care in
providing such services as it uses in providing services to
other fiduciary accounts for which it has investment
responsibilities;

	(b)	will (i) conform in all material respects to all
applicable rules and regulations of the SEC, (ii) comply in
all material respects with all policies and procedures
adopted by the Board of Trustees for the Fund and
communicated to the Sub-Adviser in writing and, (iii)
conduct its activities under this Agreement in all material
respects in accordance with any applicable law and
regulations of any governmental authority pertaining to its
investment advisory activities;
	(c)	will report to the Manager and to the Board of
Trustees of the Fund on a quarterly basis and will make
appropriate persons available for the purpose of reviewing
with representatives of the Manager and the Board of
Trustees on a regular basis at such times as the Manager or
the Board of Trustees may reasonably request in writing
regarding the management of the Fund, including, without
limitation, review of the general investment strategies of
the Fund, the performance of the Fund's investment portfolio
in relation to relevant standard industry indices and
general conditions affecting the marketplace and will
provide various other reports from time to time as
reasonably requested by the Manager or the Board of Trustees
of the Fund; and

	(d)	will prepare and maintain such books and records
with respect to the Fund's securities and other transactions
for the Fund's investment portfolio as required for
registered investment advisers under applicable law or as
otherwise requested by the  Manager and will prepare and
furnish the Manager and Fund's Board of Trustees such
periodic and special reports as the Board or the Manager may
reasonably request.  The Sub-Adviser further agrees that all
records that it maintains for the Fund are the property of
the Fund and the Sub-Adviser will surrender promptly to the
Fund any such records upon the request of the Manager or the
Fund (provided, however, that the Sub-Adviser shall be
permitted to retain copies thereof); and shall be permitted
to retain originals (with copies to the Fund) to the extent
required under Rule 204-2 of the Investment Advisers Act of
1940 or other applicable law.

	3.	Expenses.  During the term of this Agreement, the Sub-
Adviser will pay all expenses incurred by it in connection with
its activities under this Agreement other than (i) the cost of
securities and other assets purchased for the Fund, and (ii) the
costs directly associated with purchasing and selling securities
and other assets for the Fund, if any, including, but not limited
to, brokerage commissions, stamps, duties, taxes and custody fees
related to transfers.

	4.	Compensation.  For the services provided and the
expenses assumed pursuant to this Agreement, the Manager will pay
the Sub-Adviser, and the Sub-Adviser agrees to accept as full
compensation therefor, a portfolio management fee (the
"Management Fee") equal to the annual rate of 0.50% of the Fund's
Managed Assets (as defined below).  For purposes of calculating
the Management Fee, Managed Assets means the average daily gross
asset value of the Fund (including assets attributable to the
Fund's preferred shares, if any, and the principal amount of
borrowings), minus the sum of the Fund's accrued and unpaid
dividends on any outstanding preferred shares and accrued
liabilities (other than the principal amount of any borrowings
incurred, commercial paper or notes or other forms of
indebtedness issued by the Fund and the liquidation preference of
any outstanding preferred shares).  The Management Fee shall be
payable in arrears on or about the first day of each month during
the term of this Agreement.

      For the month and year in which this Agreement becomes
effective or terminates, there shall be an appropriate proration
on the basis of the number of days that the Agreement is in
effect during the month and year, respectively.

	5.	Services to Others.  The Fund and the Manager
acknowledge that the Sub-Adviser now acts, or may in the future
act, as an investment adviser to other managed accounts and as
investment adviser or sub-investment adviser to one or more other
investment companies.  In addition, the Fund and the Manager
acknowledge that the persons employed by the Sub-Adviser to
assist in the Sub-Adviser's duties under this Agreement will not
devote their full time to such efforts.  It is also agreed that
the Sub-Adviser may use any supplemental research obtained for
the benefit of the Fund in providing investment advice to its
other investment advisory accounts and for managing its own
accounts.

	6.	Limitation of Liability.  The Sub-Adviser shall not be
liable for, and the Fund and the Manager will not take any action
against the Sub-Adviser to hold the Sub-Adviser liable for, any
error of judgment or mistake of law or for any loss suffered by
the Fund or the Manager (including, without limitation, by reason
of the purchase, sale or retention of any security) in connection
with the performance of the Sub-Adviser's duties under this
Agreement, except for a loss resulting from willful misfeasance,
bad faith or gross negligence on the part of the Sub-Adviser in
the performance of its duties under this Agreement, or by reason
of its reckless disregard of its obligations and duties under
this Agreement.

	7.	Term; Termination; Amendment.  This Agreement shall
become effective with respect to the Fund on January 8, 2008 (the
"Effective Date") provided that it has been approved in the
manner required by the 1940 Act, and shall remain in full force
until June 30, 2009 unless sooner terminated as hereinafter
provided.  This Agreement, however, shall continue in force from
year to year thereafter, but only as long as such continuance is
specifically approved for the Fund at least annually in the
manner required by the 1940 Act and the rules and regulations
thereunder; provided, however, that if the continuation of this
Agreement is not approved for the Fund, the Sub-Adviser may
continue to serve in such capacity for the Fund in the manner and
to the extent permitted by the 1940 Act and the rules and
regulations thereunder.

      This Agreement shall automatically terminate in the event of
its assignment and may be terminated at any time without the
payment of any penalty by the Manager or the Sub-Adviser upon
sixty (60) days' written notice to the other parties.  This
Agreement may also be terminated by the Fund by action of the
Board of Trustees of the Fund or by a vote of a majority of the
outstanding voting securities of the Fund upon sixty (60) days'
written notice to the Sub-Adviser by the Fund without payment of
any penalty.
      This Agreement may be terminated at any time without the
payment of any penalty by the Manager, the Board of Trustees of
the Fund or by vote of a majority of the outstanding voting
securities of the Fund in the event that it shall have been
established by a court of competent jurisdiction that the Sub-
Adviser or any officer or director of the Sub-Adviser has taken
any action that results in a breach of the material covenants of
the Sub-Adviser set forth herein.

      The terms "assignment" and "vote of a majority of the
outstanding voting securities" shall have the meanings set forth
in the 1940 Act and the rules and regulations thereunder.

      Termination of this Agreement shall not affect the right of
the Sub-Adviser to receive payments on any unpaid balance of the
compensation described in Section 4 earned prior to such
termination and for any additional period during which Sub-
Adviser serves as such for the Fund, subject to applicable law.

      8.	Compliance Certification.  From time to time the Sub-
Adviser shall provide such certifications with respect to Rule
38a-1 under the 1940 Act as are reasonably requested by the Fund
or the Manager.  In addition, the Sub-Adviser will, from time to
time, provide a written assessment of its compliance program in
conformity with current industry standards that is reasonably
acceptable to the Fund to enable the Fund to fulfill its
obligations under Rule 38a-1 under the 1940 Act.

	9.	Notice.  Any notice under this Agreement shall be
sufficient in all respects if given in writing and delivered by
commercial courier providing proof of delivery and addressed as
follows or addressed to such other person or address as such
party may designate for receipt of such notice.


If to the Manager or the Fund:
If to the Sub-Adviser:
Energy Income and Growth Fund
First Trust Advisors L.P.
1001 Warrenville Road, Suite
300
Lisle, Illinois 60532
Attention:  Secretary

If by Facsimile:  (630) 241-
8650

ENERGY INCOME PARTNERS, LLC
49 Riverside Avenue
Westport, Connecticut  06880
Attention:  James J. Murchie

If by Facsimile:  (203) 286-1602

	10.	Limitations on Liability.  All parties hereto are
expressly put on notice of the Fund's Declaration of Trust and
all amendments thereto, a copy of which is on file with the
Secretary of the Commonwealth of Massachusetts, and the
limitation of shareholder and trustee liability contained therein
and a copy of which has been provided to the Sub-Adviser prior to
the date hereof.  This Agreement is executed on behalf of the
Fund by the Fund's officers in their capacity as officers and not
individually and is not binding upon any of the Trustees,
officers or shareholders of the Fund individually but the
obligations imposed upon the Fund by this Agreement are binding
only upon the assets and property of the Fund, and persons
dealing with the Fund must look solely to the assets of the Fund
for the enforcement of any claims.

	11.	Miscellaneous.  The captions in this Agreement are
included for convenience of reference only and in no way define
or delimit any of the provisions hereof or otherwise affect their
construction or effect.  This Agreement will be binding upon and
shall inure to the benefit of the parties hereto and their
respective successors.

	12.	Applicable Law.  This Agreement shall be construed in
accordance with applicable federal law and (except as to Section
10 hereof which shall be construed in accordance with the laws of
Massachusetts) the laws of the State of Illinois.

	13.	Amendment, Etc.  This Agreement may only be amended, or
its provisions modified or waived, in a writing signed by the
party against which such amendment, modification or waiver is
sought to be enforced.

	14.	Authority.  Each party represents to the others that it
is duly authorized and fully empowered to execute, deliver and
perform this Agreement.  The Fund represents that engagement of
the Sub-Adviser has been duly authorized by the Fund and is in
accordance with the Fund's Declaration of Trust and other
governing documents of the Fund.

	15.	Severability.  Each provision of this Agreement is
intended to be severable from the others so that if any provision
or term hereof is illegal or invalid for any reason whatsoever,
such illegality or invalidity shall not affect the validity of
the remaining provisions and terms hereof; provided, however,
that the provisions governing payment of the Management Fee
described in Section 4 are not severable.
	16.	Entire Agreement.  This Agreement constitutes the sole
and entire agreement of the parties hereto with respect to the
subject matter expressly set forth herein.


IN WITNESS WHEREOF, the Fund, the Manager and the Sub-Adviser
have caused this Agreement to be executed as of the day and year
first above written.

FIRST TRUST ADVISORS L.P.		ENERGY INCOME PARTNERS, LLC
By:  /s/ James A. Bowen	By:  /	s/ James J. Murchie
	James A. Bowen			James J. Murchie
	Title: President			Title:  CEO

ENERGY INCOME AND GROWTH FUND
By:  /s/ James A. Bowen
	James A. Bowen
	Title: President