FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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1. Name and Address of Reporting Person * SIMMONS L E   2. Issuer Name and Ticker or Trading Symbol OIL STATES INTERNATIONAL, INC [CPX] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director __X__ 10% Owner _____ Officer (give title below) __X__ Other (specify below) Member of Group (Last) (First) (Middle) 600 TRAVIS STREET, SUITE 6600 3. Date of Earliest Transaction (Month/Day/Year) 06/11/2008 (Street) HOUSTON, TX 77002 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) ___ Form filed by One Reporting Person _X_ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Stock 06/11/2008   S(1)   200,000 D $ 31.91 10,064,820 I By SCF-IV, L.P. (2) Common Stock 06/12/2008   S(1)   82,608 D $ 31.94 9,982,212 I By SCF-IV, L.P. (2) Common Stock               1,394,086 D   Common Stock               73,405 I By L.E. Simmons & Associates, inc. (2) Common Stock               1,049,200 I By LESFP, Ltd. (2) Common Stock               120,654 I By LES/VCWS 2005 Family Trust (2) Common Stock               681,432 I By SCF-VI, L.P. (2)

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
SIMMONS L E 600 TRAVIS STREET SUITE 6600 HOUSTON, TX 77002		X		Member of Group
SCF IV LP 600 TRAVIS STE 6600 HOUSTON, TX 77002				Member of Group
SCF VI LP 600 TRAVIS STE 6600 HOUSTON, TX 77002				Member of Group
SCF-VI, G.P., Limited Partnership 600 TRAVIS STREET SUITE 6600 HOUSTON, TX 77002				Member of Group
SIMMONS L E & ASSOCIATES INC 600 TRAVIS STE 6600 HOUSTON, TX 77002				Member of Group

Signatures

L.E. Simmons		06/13/2008
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	Represents sale of common stock of issuer held by SCF-IV, L.P.
(2)	The reporting person is sole stockholder and director of L.E. Simmons & Associates, Inc., a Delaware corporation (LESA), which is the sole general partner of SCF-IV GP LLC, of SCF-VI GP Limited Partnership (SCF-VI GP) and SCF-IV GP, both of which are Delaware limited partnerships. Additionally, SCF-VI GP is the sole general partner of SCF-VI LP (SCF-VI) and SCF-IV GP was, until the reported distribution, the sole general partner of SCF-IV. The reporting person is also the ultimate general partner of LESFP, Ltd. (LESFP) and a trustee of the LES/VCWS 2005 Family Trust (LES/VCWS 2005). Based on the reporting person's affiliation with LESFP, LES/VCWS 2005, SCF-VI GP, SCF-IV GP, SCF-IV GP LLC, SCF-VI and SCF-IV (collectively the "Related Entities"), the reporting person may be deemed to beneficially own all of the shares of common stock of the Issuer beneficially owned or deemed to be beneficially owned by the Related Entities.
Remarks: L.E. Simmons is signing for himself, as the designated filer, as well as in his capacity as attorney-in-fact for LESA, LESFP, LES/VCWS 2005, SCF-VI GP, SCF-IV GP, SCF-VI, SCF-IV GP LLC and SCF-IV.

Note: File three copies of this Form, one of which must be manually signed. If space is insufficient, see Instruction 6 for procedure.

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