Hmm, I solved this one myself, and I´ll post the solution hoping I might save others the trouble I´ve been through.
I discovered that if I not only set the ZOOM attribute, but also apply a FILTER, things work out perfectly. This is what I put in the CSS:
.Small
{
zoom: 0.80;
filter: progid

XImageTransform.Microsoft.Alpha(style=0,op acity=100);
}
And this is what I put in the HTML:
<SPAN CLASS="Small">
<IMG SRC="my_image.gif">
</SPAN>
The filter in this case is the Alpha filter, with parameters set to do just about nothing.
My theory is this: just like PaintShop Pro or other graphics software, Internet Explorer cannot do a good resize on a 256 color image. More colors are needed in order to resize for example thin lines and text. So just using ZOOM on a GIF does not work very well, at least not when my images are screen shots of dialog boxes (lots of text and thin lines). Applying a filter, however, somehow causes the the GIF to render in more than 256 colors. Otherwise effects such as blurring, opacity change, etc, could not work, right?
Again, this is just my theory. Maybe someone can confirm this? In any case, it works, although it requires a version of IE that supports both ZOOM and FILTER.
End of monologue!
/
John