I'm sure you already know how to eq, but I've found it very effective in tame a bad snare ring by setting the bandwidth as narrow as possible, cranking the gain, then sweeping the frequency until the ring is the loudest it can be, then reducing the gain until the ring is practically gone.
The ring sound is part of the "body" of the snare hit, so compression will probably make it worse. If you have a transient accentuating plugin (examples are Waves TransX or Voxengo Transmodder), this may help as it accentuates the attack, which will be more stick sound than drum sound.
I would also experiment with eq'ing out the ring before and/or after compression if you've got a computer-based rig. Hope this helps a bit...
This has turned into a good thread. A lot of people have trouble with snare ring when recording and mixing real drums.