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 [OIS] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner _____ Officer (give title below) __X__ Other (specify below) Member of Group (Last) (First) (Middle) 6600 CHASE TOWER,  3. Date of Earliest Transaction (Month/Day/Year) 06/06/2006 (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 06/06/2006   G(1)   60,000 D $ 0 136,231 D   Common Stock               1,524,160 I By SCF-III, L.P. and SCF-IV, L.P. (2) Common Stock               234,290 I By SCF-II, L.P. (2) Common Stock               23,548 I By LESFP, Ltd. (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 6600 CHASE TOWER HOUSTON, TX 77002	X			Member of Group
SCF III LP 6600 CHASE TOWER HOUSTON, TX 77002				Member of Group
SCF IV LP 600 TRAVIS STE 6600 HOUSTON, TX 77002				Member of Group
SCF II LP 600 TRAVIS STE 6600 C/O SCF PARTNERS HOUSTON, TX 77002				Member of Group
SCF IV GP LTD PARTNERSHIP 600 TRAVIS STE 6600 HOUSTON, TX 77002				Member of Group

Signatures

L.E. Simmons		06/08/2006
**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 a donation of these shares to The Church of Jesus Christ of Latter-day Saints.
(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-II LP (SCF-II), SCF-IV GP Limited Partnership (SCF-IV GP), SCF-IV 3i LP (SCFIV 3i) and SCF-IV Management Partners LP (SCF-IV MP), all of which are Delaware limited partnerships. Additionally, SCF-II is the sole general partner of SCF-III LP, a Delaware limited partnership (SCF-III) and SCF-IV GP is the sole general partner of SCF-IV LP, a Delaware limited partnership (SCF-IV). The reporting person also controls LESFP LTD (LESFP), a Delaware limited partnership. Based on the reporting person's affiliation with SCF-III, SCF-IV, SCF-II, SCF-IV GP, LESFP, SCFIV 3i, SCF-IV MP, and LESA (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, SCF-II, SCF-IV GP, SCF-III, 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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