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                                    Form 6-K

                             Washington, D.C. 20549

                        Report of Foreign Private Issuer

                        Pursuant to Rule 13a-16 or 15d-16
                     of the Securities Exchange Act of 1934

                           For the month of May, 2007

                              CONVERIUM HOLDING AG
                 (Translation of registrant's name into English)

                                 Dammstrasse 19
                                   CH-6301 Zug
                    (Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports
under cover Form 20-F or Form 40-F.

                             Form 20-F X   Form 40-F
                                      ---           ---
Indicate by check mark whether the registrant by furnishing the information
contained in this Form is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                            Yes         No    X
                                -------    -------

If "Yes" is marked, indicate the file number assigned to the registrant in
connection with Rule 12g3-2(b): 82- Not Applicable

News release
Converium Holding Ltd, Zug

Zug, Switzerland - April 27, 2007 - Converium welcomes ISS, Glass Lewis &
Co. and Ethos recommendations of approval of all tabled AGM proposals

Converium welcomes the conclusions of Institutional Shareholder Services (ISS),
which has recommended that shareholders approve all seven tabled proposals at
the Company's Annual General Meeting (AGM), scheduled for May 10, 2007. All
agenda items have been scheduled by Converium.

Amongst the proposals to be voted on at the AGM, ISS recommends approval of a
reduction of the par value of Converium's registered shares from CHF 5 to CHF
2.50, with the subsequent payment to shareholders by mid-July 2007. The ISS
acknowledges the potential to return capital to shareholders and better leverage
Converium's balance sheet through the issuance of USD 500 million of hybrid
debt, as part of the Company's road map aimed at generating a sustainable 14%
return on equity by 2009.

ISS further states that none of the voting resolutions at Converium's AGM relate
to SCOR's bid.

The guidance of ISS is in line with those of Glass Lewis & Co., which also
endorses all seven tabled AGM proposals. ISS and Glass Lewis are independent
providers of proxy voting advice to the international investment community. The
leading advisor in Switzerland on sustainable development principles and
corporate governance best practice in investment activities, Ethos, Swiss
Foundation for Sustainable Development, equally endorses all proposals.


Beat W. Werder                           Marco Circelli

Head of Public Relations                 Head of Investor Relations      

Phone:     +41 44 639 90 22              Phone:      +41 44 639 91 31

Fax:       +41 44 639 70 22              Fax:        +41 44 639 71 31

Dr. Kai-Uwe Schanz                                Inken Ehrich

Chief Communication & Corporate Development
Officer                                           Investor Relations Specialist            

Phone:     +41 44 639 90 35                       Phone:      +41 44 639 90 94

Fax:       +41 44 639 70 35                       Fax:        +41 44 639 70 94

For information regarding voting at the AGM, please contact our proxy
solicitors, HQB Partners Limited at + 44 (0)20 7621 1351.

About Converium

Converium is an independent international multi-line reinsurer known for its
innovation, professionalism and service. Today Converium employs about 500
people in 15 offices around the globe and is organized into three business
segments: Standard Property & Casualty Reinsurance, Specialty Lines and Life &
Health Reinsurance. Converium has an "A-" ("strong") financial strength rating
(outlook stable) from Standard & Poor's and a "B++" financial strength rating
(outlook positive) from A.M. Best Company.

Important Disclaimer

This document contains forward-looking statements as defined in the U.S. Private
Securities Litigation Reform Act of 1995. It contains forward-looking statements
and information relating to the Company's financial condition, results of
operations, business, strategy and plans, based on currently available
information. These statements are often, but not always, made through the use of
words or phrases such as `seek to', `expects', `aims' `should continue',
`believes', `anticipates', `estimates' and `intends'. The specific
forward-looking statements cover, among other matters, the Company's strategy
and management objectives, the reinsurance market, the Company's operating
results and SCOR's hostile tender offer. Such statements are inherently subject
to certain risks and uncertainties. Actual future results and trends could
differ materially from those set forth in such statements due to various
factors. Such factors include whether we are able to secure an upgrade of our
financial strength ratings; our ability to refinance our outstanding
indebtedness and increase our use of hybrid capital; uncertainties of
assumptions used in our reserving process; risk associated with implementing our
business strategies and our capital improvement measures; cyclicality of the
reinsurance industry; the occurrence of natural and man-made catastrophic events
with a frequency or severity exceeding our estimates; acts of terrorism and acts
of war; changes in economic conditions, including interest and currency rate
conditions that could affect our investment portfolio; actions of competitors,
including industry consolidation and development of competing financial
products; a decrease in the level of demand for our reinsurance or increased
competition in our industries or markets; our ability to expand into emerging
markets; our ability to enter into strategic investment partnerships; a loss of
our key employees or executive officers without suitable replacements being
recruited within a suitable period of time; our ability to address material
weaknesses we have identified in our internal control environment; political
risks in the countries in which we operate or in which we reinsure risks; the
passage of additional legislation or the promulgation of new regulation in a
jurisdiction in which we or our clients operate or where our subsidiaries are
organized; the effect on us and the insurance industry as a result of the
investigations being carried out by the US Securities and Exchange Commission,
New York's Attorney General and other governmental authorities; our ability to
regain past customers following any rating upgrades and the resolution of the
investigations being carried out by the US Securities and Exchange Commission,
New York's Attorney General and other governmental authorities; changes in our
investment results due to the changed composition of our invested assets or
changes in our investment policy; failure of our retrocessional reinsurers to
honor their obligations or changes in the credit worthiness of our reinsurers;
our failure to prevail in any current or future arbitration or litigation; and
extraordinary events affecting our clients, such as bankruptcies and
liquidations, and other risks and uncertainties, including those detailed in the
Company's filings with the U.S. Securities and Exchange Commission (including,
but not limited to, our Annual Report on Form 20-F filed with the U.S.
Securities and Exchange Commission) and the SWX Swiss Exchange. The Company does
not assume any obligation to update any forward-looking statements, whether as a
result of new information, future events or otherwise.


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

                              CONVERIUM HOLDING AG

                               By: /s/ Inga Beale
                                   Name:      Inga Beale
                                   Title:     CEO

                               By:  /s/ Christian Felderer
                                    Name:      Christian Felderer
                                    Title:     General Legal Counsel

Date: May 3, 2007