I can't seem to figure out how to do it.
Illustrator cannot crop raster images. It can only mask them or resort to re-rasterizing them with a silly Flatten Transparency workaround.
Thank you for your reply. Would you mind describing the Flatten Transparency workaround?
Best to crop it in an image editing software.
I was afraid of that. Oh well, it's still an awesome program.
Thanks for your help.
I am afraid James is referring to the dirty destructive deed (if he is not, silly me; if he is, also silly me; this can only be a lose/lose situation I am afraid):
With the Clipping Mask selected:
1) In the Transparency palette/panel dropdown select anything but Normal (Multiply is fine);
2) Object>Flatten Transparency (just leave it at 100% vector and other defaults).
This will rid you of the parts outside the Bounding Box of the path that shapes the Clipping Mask: a rectangle, even in case of other shapes such as ellipses, which does not hurt in your case.