Is there a good way to clean brake hoods? I just picked up an old bike with white brake hoods. They are pretty gnarsty, covered in a greyish brown layer of filth.

I've tried a soapy rag and scrubber brush with elbow grease. It takes care of most of the issue, but they're not pure clean. Is there any trick to this?
I have been using "Foaming Bathroom Cleaner" aka Scrubbing Bubbles and an old toothbruth for about two years with good results. I can't say anything about the long term results as it's only been two years. Your case might be tougher as I think the biggest tip is to clean them before the dirt gets really ground in.