8-K

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 OR 15(d) of
The Securities Exchange Act of 1934

October 4, 2005
(Date of earliest event reported)

HCC Insurance Holdings, Inc.
(Exact name of registrant as specified in its charter)

DE	001-13790	76-0336636
(State or other jurisdiction of incorporation)	(Commission File Number)	(IRS Employer Identification No.)

13403 Northwest Freeway, Houston, Texas	77040
(Address of principal executive offices)	(Zip Code)

Registrant's telephone number, including area code:   713-690-7300

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions:
	[   ]	Written communications pursuant to Rule 425 under the Securities Act (17 CFR 230.425)
	[   ]	Soliciting material pursuant to Rule 14a-12(b) under the Exchange Act (17 CFR 240.14a-12)
	[   ]	Pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))
	[   ]	Pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c))

Item 7.01 Regulation FD Disclosure

The Company issued a press release dated October 4, 2005 announcing that its 2.00% convertible notes will be convertible during the Fourth Quarter of 2005.

A copy of the press release filed by the Company is attached hereto as Exhibit 99.1 and incorporated herein by reference and is also available at HCC's website at www.hcch.com.

The information contained herein shall not be deemed "filed" for purposes of Section 18 of the Securities Exchange Act of 1934, as amended (the "Exchange Act"), or otherwise subject to the liabilities of that section, nor shall it be deemed incorporated by reference in any filing under the Securities Act of 1933, as amended, or the Exchange Act.

Item 9.01. Financial Statements and Exhibits.

    Exhibit 99.1.       Press release dated October 4, 2005

SIGNATURE

    Pursuant to the requirements of the Securities Exchange Act of 1934, as amended, the Registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.

	HCC Insurance Holdings, Inc. (Registrant)
October 4, 2005 (Date)	/s/   CHRISTOPHER L. MARTIN Christopher L. Martin Executive VP & General Counsel

Exhibit Index
99.1	Press release dated October 4, 2005

EX-99.1

EXHIBIT 99.1

HCC Announces Conversion Rights of Its 2 Percent Convertible Notes

HOUSTON, Oct. 4, 2005 (PRIMEZONE) -- HCC Insurance Holdings, Inc. (NYSE:HCC) announced today that based upon its share performance during the Third Quarter 2005, its originally issued and exchanged 2.00% Convertible Notes due 2021 (collectively, the "2% Notes") will be convertible under the terms of their respective Indentures during the Fourth Quarter 2005.

Holders of the 2% Notes may obtain information on how to convert their notes by contacting the Conversion Agent at:

 Wachovia Bank, National Association
 5847 San Felipe, Suite 1050,
 Houston, Texas 77057,
 Attention: Stephanie Moore
 Tel: (713) 278-4320

HCC is an international insurance holding company and a leading specialty insurance group since 1974, based in Houston, Texas with offices across the USA and in Bermuda, England and Spain. HCC has assets exceeding $6.0 billion and is rated AA (Very Strong) by Standard & Poor's and A+ (Superior) by A. M. Best Company.

For more information, visit our website at www.hcch.com.

Forward-looking statements contained in this press release are made under "safe harbor" provisions of the Private Securities Litigation Reform Act of 1995 and involve a number of risks and uncertainties. The types of risks and uncertainties which may affect the Company are set forth in its periodic reports filed with the Securities and Exchange Commission.

CONTACT:  HCC Insurance Holdings, Inc.
          L. Byron Way, Vice President
          (713) 690-7300