UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

SCHEDULE 13G

Under the Securities Exchange Act of 1934

(Amendment No. ___________)*

Bronco Drilling Company, Inc. (the “Issuer”)

(Name of Issuer)

Common Stock, par value $0.01 per share (“Common Shares”)

(Title of Class of Securities)

112211107

(CUSIP Number)

October 15, 2008

(Date of Event Which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this Schedule is filed:

o Rule 13d-1(b)

x Rule 13d-1(c)

o Rule 13d-1(d)

^*The remainder of this cover page shall be filled out for a reporting person’s initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the Securities Exchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

CUSIP No. 112211107

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1	NAMES OF REPORTING PERSONS I.R.S. IDENTIFICATION NO. OF ABOVE PERSON (ENTITIES ONLY)
	Carlos Slim Helú
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP* (a) o (b) o
3	SEC USE ONLY
4	CITIZENSHIP OR PLACE OF ORGANIZATION
	México
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH		5	SOLE VOTING POWER
		6	SHARED VOTING POWER 2,200,000 Common Shares (see Item 4(c))
		7	SOLE DISPOSITIVE POWER
		8	SHARED DISPOSITIVE POWER 2,200,000 Common Shares (see Item 4(c))
9	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 2,200,000 Common Shares (see Item 4(a))
10	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES o*
11	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9 7.636% (see Item 4(b))
12	TYPE OF REPORTING PERSON* IN
*SEE INSTRUCTIONS BEFORE FILLING OUT!

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1	NAMES OF REPORTING PERSONS I.R.S. IDENTIFICATION NO. OF ABOVE PERSON (ENTITIES ONLY)
	Carlos Slim Domit
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP* (a) o (b) o
3	SEC USE ONLY
4	CITIZENSHIP OR PLACE OF ORGANIZATION
	México
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH		5	SOLE VOTING POWER
		6	SHARED VOTING POWER 2,200,000 Common Shares (see Item 4(c))
		7	SOLE DISPOSITIVE POWER
		8	SHARED DISPOSITIVE POWER 2,200,000 Common Shares (see Item 4(c))
9	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 2,200,000 Common Shares (see Item 4(a))
10	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES o*
11	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9 7.636% (see Item 4(b))
12	TYPE OF REPORTING PERSON* IN
*SEE INSTRUCTIONS BEFORE FILLING OUT!

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1	NAMES OF REPORTING PERSONS I.R.S. IDENTIFICATION NO. OF ABOVE PERSON (ENTITIES ONLY)
	Marco Antonio Slim Domit
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP* (a) o (b) o
3	SEC USE ONLY
4	CITIZENSHIP OR PLACE OF ORGANIZATION
	México
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH		5	SOLE VOTING POWER
		6	SHARED VOTING POWER 2,200,000 Common Shares (see Item 4(c))
		7	SOLE DISPOSITIVE POWER
		8	SHARED DISPOSITIVE POWER 2,200,000 Common Shares (see Item 4(c))
9	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 2,200,000 Common Shares (see Item 4(a))
10	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES o*
11	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9 7.636% (see Item 4(b))
12	TYPE OF REPORTING PERSON* IN
*SEE INSTRUCTIONS BEFORE FILLING OUT!

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1	NAMES OF REPORTING PERSONS I.R.S. IDENTIFICATION NO. OF ABOVE PERSON (ENTITIES ONLY)
	Patrick Slim Domit
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP* (a) o (b) o
3	SEC USE ONLY
4	CITIZENSHIP OR PLACE OF ORGANIZATION
	México
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH		5	SOLE VOTING POWER
		6	SHARED VOTING POWER 2,200,000 Common Shares (see Item 4(c))
		7	SOLE DISPOSITIVE POWER
		8	SHARED DISPOSITIVE POWER 2,200,000 Common Shares (see Item 4(c))
9	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 2,200,000 Common Shares (see Item 4(a))
10	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES o*
11	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9 7.636% (see Item 4(b))
12	TYPE OF REPORTING PERSON* IN
*SEE INSTRUCTIONS BEFORE FILLING OUT!

CUSIP No. 112211107

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1	NAMES OF REPORTING PERSONS I.R.S. IDENTIFICATION NO. OF ABOVE PERSON (ENTITIES ONLY)
	María Soumaya Slim Domit
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP* (a) o (b) o
3	SEC USE ONLY
4	CITIZENSHIP OR PLACE OF ORGANIZATION
	México
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH		5	SOLE VOTING POWER
		6	SHARED VOTING POWER 2,200,000 Common Shares (see Item 4(c))
		7	SOLE DISPOSITIVE POWER
		8	SHARED DISPOSITIVE POWER 2,200,000 Common Shares (see Item 4(c))
9	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 2,200,000 Common Shares (see Item 4(a))
10	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES o*
11	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9 7.636% (see Item 4(b))
12	TYPE OF REPORTING PERSON* IN
*SEE INSTRUCTIONS BEFORE FILLING OUT!

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1	NAMES OF REPORTING PERSONS I.R.S. IDENTIFICATION NO. OF ABOVE PERSON (ENTITIES ONLY)
	Vanessa Paola Slim Domit
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP* (a) o (b) o
3	SEC USE ONLY
4	CITIZENSHIP OR PLACE OF ORGANIZATION
	México
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH		5	SOLE VOTING POWER
		6	SHARED VOTING POWER 2,200,000 Common Shares (see Item 4(c))
		7	SOLE DISPOSITIVE POWER
		8	SHARED DISPOSITIVE POWER 2,200,000 Common Shares (see Item 4(c))
9	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 2,200,000 Common Shares (see Item 4(a))
10	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES o*
11	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9 7.636% (see Item 4(b))
12	TYPE OF REPORTING PERSON* IN
*SEE INSTRUCTIONS BEFORE FILLING OUT!

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1	NAMES OF REPORTING PERSONS I.R.S. IDENTIFICATION NO. OF ABOVE PERSON (ENTITIES ONLY)
	Johanna Monique Slim Domit
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP* (a) o (b) o
3	SEC USE ONLY
4	CITIZENSHIP OR PLACE OF ORGANIZATION
	México
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH		5	SOLE VOTING POWER
		6	SHARED VOTING POWER 2,200,000 Common Shares (see Item 4(c))
		7	SOLE DISPOSITIVE POWER
		8	SHARED DISPOSITIVE POWER 2,200,000 Common Shares (see Item 4(c))
9	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 2,200,000 Common Shares (see Item 4(a))
10	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES o*
11	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9 7.636% (see Item 4(b))
12	TYPE OF REPORTING PERSON* IN
*SEE INSTRUCTIONS BEFORE FILLING OUT!

CUSIP No. 112211107

Page 9 of 24 Pages

1	NAMES OF REPORTING PERSONS I.R.S. IDENTIFICATION NO. OF ABOVE PERSON (ENTITIES ONLY)
	Inmobiliaria Carso, S.A. de C.V.
2	CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP* (a) o (b) o
3	SEC USE ONLY
4	CITIZENSHIP OR PLACE OF ORGANIZATION
	México
NUMBER OF SHARES BENEFICIALLY OWNED BY EACH REPORTING PERSON WITH		5	SOLE VOTING POWER
		6	SHARED VOTING POWER 2,200,000 Common Shares (see Item 4(c))
		7	SOLE DISPOSITIVE POWER
		8	SHARED DISPOSITIVE POWER 2,200,000 Common Shares (see Item 4(c))
9	AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON 2,200,000 Common Shares (see Item 4(a))
10	CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES o*
11	PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9 7.636% (see Item 4(b))
12	TYPE OF REPORTING PERSON* HC
*SEE INSTRUCTIONS BEFORE FILLING OUT!

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Item 1.
(a)	Name of Issuer: Bronco Drilling Company, Inc. (the “Issuer”)
(b)	Address of Issuer’s Principal Executive Offices: 16217 North May Avenue Edmond, OK 73013
Item 2.
(a)	Name of Persons Filing: This statement is filed pursuant to Rule 13d-1(c) under the Securities Exchange Act of 1934, as amended (the “Act”), by the persons listed below (the “Reporting Persons”). (1) Carlos Slim Helú, Carlos Slim Domit, Marco Antonio Slim Domit, Patrick Slim Domit, María Soumaya Slim Domit, Vanessa Paola Slim Domit and Johanna Monique Slim Domit (collectively, the “Slim Family”), each of whom is a Mexican citizen. The members of the Slim Family are beneficiaries of a Mexican trust which in turn owns all of the outstanding voting securities of Inmobiliaria Carso, S.A. de C.V (“Inmobiliaria”). (2) Inmobiliaria, a sociedad anónima de capital variable organized under the laws of the United Mexican States (“Mexico”), is a holding company with portfolio investments in various companies.


(b)	Address of Principal Business Office: (i) The principal business address for each member of the Slim Family is: Paseo de las Palmas 736 Colonia Lomas de Chapultepec 11000 México, D.F., México (ii) Inmobiliaria’s principal business address is: Avenida Insurgentes Sur #3500, PB Colonia Peña Pobre Delegación Tlalpan, CP 14060 México D.F. México
(c)	Citizenship: Each member of the Slim Family is a Mexican citizen and Inmobiliaria is a Mexican corporation.

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(d)	Title of Class of Securities: Common Stock, par value $0.01 per share (“Common Shares”)
(e)	CUSIP Number: 112211107
Item 3.	If this statement is filed pursuant to Rule 13d-1(b), or 13d-2(b) or (c), check whether the person filing is a(n):
(a)		Broker or dealer registered under Section 15 of the Act;

(b)		Bank as defined in Section 3(a)(6) of the Act;

(c)		Insurance company as defined in Section 3(a)(19) of the Act;

(d)		Investment company registered under Section 8 of the Investment Company Act;

(e)		Investment adviser in accordance with Rule 13d-1(b)(1)(ii)(E);

(f)		Employee benefit plan or endowment fund in accordance with Rule 13d-1(b)(1)(ii)(F);

(g)		Parent holding company or control person in accordance with Rule 13d-1(b)(1)(ii)(G);

(h)		Savings association as defined in Section 3(b) of the Federal Deposit Insurance Act;

CUSIP No. 112211107

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(i)		Church plan that is excluded from the definition of an investment company under Section 3(c)(14) of the Investment Company Act; or

(j)		Group, in accordance with Rule 13d-1(b)(1)(ii)(J).
Item 4.	Ownership.
(a)	Amount Beneficially Owned: As of October 22, 2008, (i) Inmobiliaria directly or indirectly owns 2,200,000 Common Shares, and (ii) the Slim Family, which owns all of the issued and outstanding voting equity securities of Inmobiliaria, may be deemed to beneficially own indirectly the Common Shares beneficially owned directly or indirectly by Inmobiliaria.
(b)	Percent of Class: The Common Shares beneficially owned by the Reporting Persons constitute approximately 7.636%% of the 28,809,751 issued and outstanding Common Shares, as reported in the Form 10-Q filed by the Issuer with the Securities and Exchange Commission on August 8, 2008.

(c)	Number of shares as to which such person has:
	(i)		Sole power to vote or to direct the vote: -0-
	(ii)		Shared power to vote or to direct the vote: 2,200,000 Common Shares
	(iii)		Sole power to dispose or to direct the disposition of: -0-
	(iv)		Shared power to dispose or direct the disposition of: 2,200,000 Common Shares
Item 5.	Ownership of Five Percent or Less of a Class.
	If this statement is being filed to report the fact that as of the date hereof the reporting person has ceased to be the beneficial owner of more than five percent of the class of securities, check the following:			o

Item 6.	Ownership of More than Five Percent on Behalf of Another Person. Not applicable.
Item 7.	Identification and Classification of the Subsidiary Which Acquired the Security Being Reported on by the Parent Holding Company. Not applicable.
Item 8.	Identification and Classification of Members of the Group. Not applicable.
Item 9.	Notice of Dissolution of Group. Not applicable.

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Item 10.	Certifications.
	By signing below I certify that, to the best of my knowledge and belief, the securities referred to above were not acquired and are not held for the purpose of or with the effect of changing or influencing the control of the issuer of the securities and were not acquired and are not held in connection with or as a participant in any transaction having that purpose or effect.

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SIGNATURE

After reasonable inquiry and to the best of my knowledge and belief I certify that the information set forth in this statement is true, complete and correct.

Carlos Slim Helú
_____________________________
Carlos Slim Domit	By: /s/ Eduardo Valdés Acra
_____________________________	Eduardo Valdés Acra
Marco Antonio Slim Domit	Attorney-in-Fact
_____________________________	October 22, 2008
Patrick Slim Domit
_____________________________
María Soumaya Slim Domit
_____________________________
Vanessa Paola Slim Domit
_____________________________
Johanna Monique Slim Domit


INMOBILIARIA CARSO, S.A. DE C.V.
_____________________________
By: Armando Ibáñez Vázquez
Title: Attorney-in-Fact

CUSIP No. 112211107

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POWER OF ATTORNEY

The undersigned hereby constitutes and appoints Eduardo Valdés Acra and Rafael Robles Miaja, and each of them singly, as his true and lawful attorney-in-fact and agent, with full power of substitution and resubstitution, to act for him and in his name, place and stead and on his behalf, in any and all capacities, to sign any Form 3, 4 or 5 or Schedule 13D or 13G, and any and all amendments thereto and any other document relating thereto (including any joint filing agreement) (each a “Filing”), relating to his beneficial ownership (direct or indirect) of any securities he may be deemed to beneficially own, and to file on his behalf any such Filings required to be filed pursuant to the United States Securities Exchange Act of 1934, as amended, with the United States Securities and Exchange Commission, hereby granting unto said attorneys-in-fact and agents full power and authority to do and perform any and all acts and things requisite as fully to all intents and purposes as he might or could do in person, hereby ratifying and confirming all that said attorneys-in-fact and agents may lawfully do or cause to be done by virtue hereof, and this power of attorney shall be irrevocable until December 31, 2008.

March 19, 2004

	/s/ Carlos Slim Helú
	Carlos Slim Helú

CUSIP No. 112211107

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POWER OF ATTORNEY

March 19, 2004

	/s/ Carlos Slim Domit
	Carlos Slim Domit

CUSIP No. 112211107

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POWER OF ATTORNEY

March 19, 2004

	/s/ Marco Antonio Slim Domit
	Marco Antonio Slim Domit

CUSIP No. 112211107

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POWER OF ATTORNEY

March 19, 2004

	/s/ Patrick Slim Domit
	Patrick Slim Domit

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POWER OF ATTORNEY

The undersigned hereby constitutes and appoints Eduardo Valdés Acra and Rafael Robles Miaja, and each of them singly, as her true and lawful attorney-in-fact and agent, with full power of substitution and resubstitution, to act for her and in her name, place and stead and on her behalf, in any and all capacities, to sign any Form 3, 4 or 5 or Schedule 13D or 13G, and any and all amendments thereto and any other document relating thereto (including any joint filing agreement) (each a “Filing”), relating to her beneficial ownership (direct or indirect) of any securities she may be deemed to beneficially own, and to file on her behalf any such Filings required to be filed pursuant to the United States Securities Exchange Act of 1934, as amended, with the United States Securities and Exchange Commission, hereby granting unto said attorneys-in-fact and agents full power and authority to do and perform any and all acts and things requisite as fully to all intents and purposes as she might or could do in person, hereby ratifying and confirming all that said attorneys-in-fact and agents may lawfully do or cause to be done by virtue hereof, and this power of attorney shall be irrevocable until December 31, 2008.

March 19, 2004

	/s/ María Soumaya Slim Domit
	María Soumaya Slim Domit

CUSIP No. 112211107

Page 20 of 23 Pages

POWER OF ATTORNEY

March 19, 2004

	/s/ Vanessa Paola Slim Domit
	Vanessa Paola Slim Domit

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POWER OF ATTORNEY

March 19, 2004

	/s/ Johanna Monique Slim Domit
	Johanna Monique Slim Domit

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POWER OF ATTORNEY

The undersigned, an authorized officer of Inmobiliaria Carso, S.A. de C.V. (the “Company”), hereby constitutes and appoints Eduardo Valdés Acra and Rafael Robles Miaja, and each of them singly, as the Company’s true and lawful attorney-in-fact and agent, with full power of substitution and resubstitution, to act for the Company and in the Company’s name, place and stead and on the Company’s behalf, in any and all capacities, to sign any Form 3, 4, or 5 or Schedule 13D or 13G, and any and all amendments thereto and any other document relating thereto (including any joint filing agreement) (each a “Filing”), relating to the Company’s beneficial ownership (direct or indirect) of any securities it may be deemed to beneficially own, and to file on the Company’s behalf any such Filings required to be filed pursuant to the United States Securities Exchange Act of 1934, as amended, with the United States Securities and Exchange Commission, hereby granting unto said attorneys-in-fact and agents, full power and authority to do and perform any and all acts and things requisite as fully to all intents and purposes as the Company might or could do in person, hereby ratifying and confirming all that said attorneys-in-fact and agents may lawfully do or cause to be done by virtue hereof, and this power of attorney shall be irrevocable until December 31, 2008.

February 4, 2004

	INMOBILIARIA CARSO, S.A. DE C.V.
	/s/ Armando Ibañez Vazquez
	By: Armando Ibañez Vazquez Title: Attorney-in-Fact

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JOINT FILING AGREEMENT

THIS JOINT FILING AGREEMENT (this “Agreement”) is made and entered into as of this 22nd day of October 2008, by and among Carlos Slim Helú, Carlos Slim Domit, Marco Antonio Slim Domit, Patrick Slim Domit, María Soumaya Slim Domit, Vanessa Paola Slim Domit, Johanna Monique Slim Domit and Inmobiliaria Carso, S.A. de C.V.

The parties to this Agreement hereby agree to prepare jointly and file timely (and otherwise to deliver as appropriate) all filings on any Form 3, 4 or 5 or Schedule 13D or 13G relating to their ownership (direct or otherwise) of any securities of Bronco Drilling Company, Inc., a corporation organized under the laws of Delaware, and any and all amendments thereto and any other document relating thereto (collectively, the “Filings”) required to be filed by them pursuant to the Securities Exchange Act of 1934, as amended. Each party to this Agreement further agrees and covenants to the other parties that it will fully cooperate with such other parties in the preparation and timely filing (and other delivery) of all such Filings.

IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date first set forth above.

Carlos Slim Helú
________________________________
Carlos Slim Domit	By: /s/ Eduardo Valdés Acra
________________________________	Eduardo Valdés Acra
Marco Antonio Slim Domit	Attorney-in-Fact
________________________________	October 22, 2008
Patrick Slim Domit
________________________________
María Soumaya Slim Domit
________________________________
Vanessa Paola Slim Domit
________________________________
Johanna Monique Slim Domit
________________________________

INMOBILIARIA CARSO, S.A. DE C.V.
________________________________
By: Armando Ibáñez Vázquez
Title: Attorney-in-Fact