George, Bryce
The original problem was that when I converted a png file to a gif or jpg (so as to keep the file size small), then areas that were transparent and showing detail below were going opaque and not showing that underlying detail.  Images were therefore losing their purpose.  (This may just have been a bad day for me at the computer!  No, it wasn't - I have just tried Fireworks and Photoshop and they won't read the Inkscape transparency of a png file correctly for me.)
As you say, the real solution is to concentrate on compression of the png files - how is it best to do that?  I am on Windows XP Home edition.  I have tried something called Irfanview and it does not read the png file correctly - loses transparency.