SECTION 906 CERTIFICATION


         Pursuant to 18 U.S.C. Section 1350, each of the undersigned officers of
Calamos Convertible and High Income Fund (the "Company"), hereby certifies, to
his knowledge, that the Company's Report on Form N-CSR for the year ended
October 31, 2004 (the "Report") fully complies with the requirements of Section
13(a) or 15(d), as applicable, of the Securities Exchange Act of 1934 and that
the information contained in the Report fairly presents, in all material
respects, the financial condition and results of operations of the Company.

Date:

/s/ John P. Calamos, Sr.
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Name:  John P. Calamos, Sr.
Title: Principal Executive Officer



/s/ Patrick H. Dudasik
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Name:  Patrick H. Dudasik
Title: Principal Financial Officer


This certificate is furnished pursuant to the requirements of Form N-CSR and
shall not be deemed "filed" for purposes of section 18 of the Securities
Exchange Act of 1934, or otherwise subject to the liability of that section, and
shall not be deemed to be incorporated by reference into any filing under the
Securities Act of 1933 or the Exchange Act of 1934.

A signed original of this certificate required by Section 906 has been provided
to Calamos Convertible and High Income Fund and will be retained by Calamos
Convertible and High Income Fund and furnished to the Securities and Exchange
Commission or staff upon request.




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