I've tried various combinations of fuzz, draw, etc. In general I'm using:
convert espn_u.eps -flatten -bordercolor white -border 1x1 -matte -fill none -fuzz 20% -draw "matte 1,1 floodfill" -shave 1x1 -trim -strip espn_u.gif
The source file is:
http://www.tvpassport.com/tvmds/grid/im ... espn_u.eps
Before (just convert -flatten espn_u.eps espn_u.gif):

After:

Any advice?