Fixing Lifted Wood on Dresser

You might put wax paper between the wood and the cookie sheet too.

You can redampen it if you need to in order to be able to GENTLY get underneath with some glue. My carpenter son uses Gorilla Glue and says it WILL NOT move again. Just squirt some under there and press it down in place then weight it down with something. I would use a cookie sheet with books on top. I wouldn't put books directly on it just in case there was some leakage around the edges. Be sure to wipe up any that does dribble out before it hardens.