I uploaded some GIFs with transparent backgrounds and inserted them in page at a reduced size. The transparent parts appeared as black both in the media library and in the post. There is a post on this forum from 2009 describing the same problem, but I am using the current version of WordPress. I suspect that the problem is that the "crunching" process discards transprency information.
The page in question (still a work in progress) is at http://john-s-allen.com/streetsmarts/?page_id=39. The three images displaying the problem are in the body of the page -- scroll down to find them. The area where the lozenge shape for the word "right" or "wrong" extends outside the image should be transparent.
The blog I need help with is john-s-allen.com.