It is of the nature of raster images they cannot change size with impunity.
If you have your logo in a vector format, like SVG, or postscript, you better use another program to generate a low resolution version of it.
Otherwise, if the original is raster, them one way to try to reduce it is to downscale it a bit of a time (around 10%), and run enhance-filters at each step. It will yield you a better result, but still far from perfect.
You can do that programatically - open up a Python console in filters->python->console
Then, retrieve a reference to your image with:
img = gimp.image_list()[0]
(the 0
) referes to the last image tab open - use "1" for the one before that, and so on.
And them just type:
while img.width > 80:
pdb.gimp_image_scale(img, int(img.width * 0.9), int(img.height * 0.9))
pdb.plug_in_unsharp_mask(img, img.layers[0], 3, 0.5, 4)
(If you know nothing about Python: beware of the identation - the two lines inside the while
must have a common whitespace prefix - and hit in a blank line to actually execute it)