Blurred shadow without banding

Hi!  I need to produce graphics (logos, text)
with a grey shadow.  The shadow has to be blurred.
My problem is when I reduce the number of colors
to make it a GIF file the shadows show bands or
when I dither it they come out spotted.

I've seen some GIF graphics on the web where the
grey shadows appear smoothly blurred.  The only
example that comes to mind right now however is
the AOL instant messenger logo.
Again the graphic needs to be a GIF not JPEG.
I have experimented with the web-safe grey
colors and different blurring levels but no luck.

TIA
Jerry

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