and it's an excellent suggestion, here are a couple of other things you can try:
1. Citrus (peels mostly): oranges, lemons, limes, etc. Put these in the disposer and grind them up WITHOUT adding water for about the first 30 seconds or so, then just add a trickle of water until the disposer clears. The citric acid will help get rid of some of that residue David mentioned.
2. Commercial disposal cleaners. There are several on the market and are sold where you buy your dishwasher detergent. Usually they are a paper packet that you put into the disposal, turn on a a very slow trickle of water, start the disposal, and they foam up. When the foam comes up out of the drain, you turn off the water and just let it do its thing until the foam completely dissappears (about 10 minutes). Then you turn the water and disposer back on to wash the whole mess away. Clean and shining.