Form 8-K Filing

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

Date of Report (Date of earliest event reported) April 3, 2006

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



________________________________________________________________________________
(Former name or former address, if changed since last report)



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 April 3, 2006 announcing that its 2.00% convertible notes and its 1.30% convertible notes will be convertible during the First Quarter of 2006.

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 April 3, 2006

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)
April 3, 2006
(Date) 		  /s/   CHRISTOPHER L. MARTIN
Christopher L. Martin
Executive VP & General Counsel

  Exhibit Index
  99.1 Press release dated April 3, 2006