Why is image file size increasing when changed to CMYK?

When converting the colour of a Jpeg to CMYK in Photoshop CS5 the file size is increasing.
The original image is 352KB and after saving as CMYK it is 2.1MB
Why is this happening and how can I stop it?
I'm using a lot of images for a print project so need to keep file sizes small with resolution of 300dpi. The image dimensions are really small, only about 30mm high so they shouldn't be this large a file size
I am using a clipping path but this doesn't seem to be effecting file size (I checked by saving it as RGB with a clipping path which stayed small, and by saving one without a clipping path in CMYK which was huge)
Thanks

Two things may be happening:
1)      you may be making the file pixel dimensions (width and height) larger due to the 300 dpi requirement.
2)      CMYK files, with 4 colors per pixel, are expected to be larger than JPG files, which are 3 colors per pixel and the data is compressed in a way that throws away information.
You will not get CMYK files anywhere near as small as JPG files, as you are finding.   If there are compression options available when you save the file, perhaps those can make the files smaller.
What pixel dimensions is the original JPG and what pixel dimensions are the CYMK files?

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