[GarySP]

Just re-read your post.  Nail AND glue the trim to the tops.  One more hint... use a pair of needle-nosed pliers to hold the nails when you nail the trim.  Saves wear and tear on the fingers beating them with a hammer!  Chuck one of the nails into a drill and use it to pre-drill holes in the trim to avoid splitting.  Cut the head off the nail if it won't chuck into the drill cleanly.  Take care, Gary