Hey buckrod, your friends are correct. Hydrogen peroxide gives the most pleasing results on old wheaties, but takes a long soak to loosen up the dirt, etc. Here's another thought, you might want to try washing soda (arm and hammer makes it, in the laundry soap section of any supermarket). Put into a glass vessel or plastic, some boiling water, couple tablespoons of the soda powder, and aluminum foil. I usually put a small sheet of aluminum first and line the bottom, coins on top, then add the water and soda. The aluminum is a catalyst to the reaction and makes it work faster and with more vigor. Cleaning achieved is usually somewhat gentle on copper, you might want to try a few wheaties alone first, and see if you like the results.
Hope this helps,
Mark