The cleaning of an LP jacket

I hadn't bought a used LP in a while, but did today. The LP itself is pretty clean, and will be even cleaner after it gets washed. But the cardboard jacket (cover) is a little nasty, more so than the ones I usually buy. What methods and products have all ya'll used to get them clean? With my normal not-so-dirty ones, I've always just set the jacket on the kitchen or dining room table and rubbed it with a folded paper towel. This cover looks like more drastic measures might be required to get the grime off.