imagemagick convert: changing color profile

I use the imagemagick convert command to create thumbnails for the web from large images.

convert y2.psd[0] -resize '80x40' y2.png

Some images uploaded by a customer are CMYK Photoshop files with very large custom icc profiles. A 3Mbyte photoshop file turned into a 1.2Mbyte png file, even though the output png size was 80x40. The rest of the png file seems to have been profile information. When I run

convert y2.png -strip y2stripped.png

the file size goes down from 1.2Mbytes to 2kbytes.

I'm not too worried about including any profile information with the thumbnail, but I would like to know that the png has been properly produced and does reasonably represent the original image. I can't find any information on telling convert what color profile to use for the output image. Is color profile handling in convert well defined, please? How do I ask it to produce output with a specific color profile?