Exhibit 10.1

FIRST AMENDMENT TO
COOPER CAMERON CORPORATION
2005 EQUITY INCENTIVE PLAN

WHEREAS, COOPER CAMERON CORPORATION (the “Company”) has heretofore adopted the
2005 EQUITY INCENTIVE PLAN (the EQIP Plan); and

WHEREAS, the Company desires to amend the 2005 Equity Incentive Plan in certain
respects;

NOW, THEREFORE, the 2005 Equity Incentive Plan shall be amended as follows,
effective as of February 15, 2006:

  1.   Section 7.4 of the 2005 Equity Incentive Plan be and hereby is amended by
adding, in the seventh line thereof following the word “employer,” the following
words:  

“(so long as the cumulative total of any such grants does not exceed five
percent (5%) of the total number of  shares subject to the Plan)”

  2.   As amended hereby, the Plan is specifically ratified and affirmed.  

APPROVED:

/s/ William C. Lemmer
     
William C. Lemmer
Vice President, General Counsel
and Secretary

Date: February 15, 2006