Tell him you have been seeing mice because of the food he leaves around. Lying is lying, but sometimes creative story telling is necessary.
My 3-year old nephew would stand in a chair and get five popsicles out of the freezer everyday. If one was a flavor he didn't like, he would just throw it down on his bed. They put a lock on the freezer, but he figured out how to unlock it. His parents also tried to hide the candy and cookies, but he always found them and ate like there was no tomorrow.
If your son is willing to go to nutrition counseling, it might help. Most insurance plans cover it now.
