Exhibit 10.12

GEOMET, INC.

Amendment No. 1

To

2006 Long-Term Incentive Plan

THIS AMENDMENT NO. 1 (this “Amendment”) to the 2006 Long-Term Incentive Plan
(the “Plan”), of GEOMET, INC., a Delaware corporation (the “Company”),
originally adopted effective April 17, 2006, is herein adopted effective
March 13, 2007;

WHEREAS, the Board of Directors of the Company has approved non-material
amendments to the Plan to provide that “Fair Market Value” as defined thereunder
shall be based upon the closing price (rather than the average of the highest
and lowest selling prices) of a share of the Company’s Common Stock and to
provide that “Corporate Change” as defined thereunder shall not include private
offerings of the Company’s Common Stock;

NOW, THEREFORE, the Plan shall be amended as follows:

1. Defined Terms. Capitalized terms used but not defined herein shall have the
meanings given such terms in the Plan.

2. Amendment. Section 2.11 and Section 2.16 of the Plan are hereby amended in
their entirety so that, as amended, said Sections 2.11 and 2.16 shall read as
follows:

“2.11 “Corporate Change” means (a) the dissolution or liquidation of GeoMet;
(b) a reorganization, merger or consolidation of GeoMet with one or more
corporations (other than a merger or consolidation effecting a reincorporation
of GeoMet in another state or any other merger or consolidation in which the
stockholders of the surviving corporation and their proportionate interests
therein immediately after the merger or consolidation are substantially
identical to the stockholders of GeoMet and their proportionate interests
therein immediately prior to the merger or consolidation) (collectively, a
“Corporate Change Merger”); (c) the sale of all or substantially all of the
assets of the Company; or (d) the occurrence of a Change in Control.
Notwithstanding the foregoing, “Corporate Change” shall not include the Offering
or any public offering of equity of GeoMet pursuant to a registration that is
effective under the Securities Act or any private offering of equity of GeoMet
pursuant to an exemption from the Securities Act. A “Change in Control” shall be
deemed to have occurred if (a) individuals who were directors of GeoMet
immediately prior to a Control Transaction shall cease, within two years of such
Control Transaction to constitute a majority of the Board (or of the Board of
Directors of any successor to GeoMet or to a company which has acquired all or
substantially all its assets) other than by reason of an increase in the size of
the membership of the applicable Board that is approved by at least a majority
of the

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individuals who were directors of GeoMet immediately prior to such Control
Transaction or (b) any entity, person or Group acquires shares of GeoMet in a
transaction or series of transactions that result in such entity, person or
Group directly or indirectly owning beneficially 50% or more of the outstanding
shares of Common Stock. As used herein, “Control Transaction” means (a) any
tender offer for or acquisition of capital stock of GeoMet pursuant to which any
person, entity, or Group directly or indirectly acquires beneficial ownership of
20% or more of the outstanding shares of Common Stock; (b) any Corporate Change
Merger of GeoMet; (c) any contested election of directors of GeoMet; or (d) any
combination of the foregoing, any one of which results in a change in voting
power sufficient to elect a majority of the Board. As used herein, “Group” means
persons who act “in concert” as described in Sections 13(d)(3) and/or 14(d)(2)
of the Exchange Act.”

“2.16 “Fair Market Value” means (a) for so long as the Common Stock is listed on
the NASDAQ Global Market or other exchange or association on which the Common
Stock is traded, the closing price for such stock as quoted on such exchange for
the date the Award is granted (or if there are no sales for such date of grant,
then for the last preceding business day on which there were sales), (b) if the
Common Stock is traded in the over-the-counter market, the closing price as
reported by NASDAQ on for the date the Award is granted (or if there was no
quoted price for such date of grant, then for the last preceding business day on
which there was a quoted price), or (c) if the Common Stock is not reported or
quoted by any such organization, fair market value of the Common Stock as
determined in good faith by the Committee using a “reasonable application of a
reasonable valuation method” within the meaning Section 409A of the Code and the
regulations thereunder. Notwithstanding the foregoing, “Fair Market Value” with
respect to an Incentive Stock Option shall mean fair market value as determined
in good faith by the Committee within the meaning of Section 422 of the Code.”

3. Nature of Amendment. In accordance with Section 14.1 of the Plan, the Board
has determined that this Amendment shall not require approval of the
shareholders of the Company and therefore this Amendment shall become effective
as of the date that the Board has approved this Amendment, as shown below.

4. Ratification. As amended hereby, the Plan in hereby ratified and confirmed.

IN WITNESS WHEREOF, this Amendment has been executed on behalf of the Company by
authority of the Board of Directors as of March 13, 2007.

 

GEOMET, INC. By:  

/s/ J. Darby Seré

  J. DARBY SERÉ, Chairman, President and Chief Executive Officer

 

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