That is a great idea if it is just cats and squirrels. But i am pretty sure mice and probably chipmunks can still find a way in. I don't find it to be a problem during the summer as much as I do the winter and grills that get used regular don't seem to have the problem where I am at. But, when I leave grills out over the winter, there is a VERY good chance I will have a nest in the bottom drip pan come spring. Dropping a sheet of BOUNCE dryer sheets in side the grill solves the problem. I had six grills out back this winter and none of them had a nest this spring. Has to be BOUNCE brand though. This probably isn't an option during the summer though. The odor from the sheet doesn't mix well with hickory smoke...LOL
Maybe you could drop one inside the bottom of the cabinet, but that might still be a problem with odor.
