How do I flatten a cupped tabletop panel?

I left the unfinished top for a blanket chest in my truck on a hot, humid day, and it cupped. Can I get the top flat again without planing it (and reducing thickness)?
—Paul Salisbury, Waukee, Iowa

Before trying anything else, Paul, try reversing the process by putting it back in the truck with the opposite face up (cupped face down) for a similar amount of time and in similar conditions. That might equalize things and reverse the cup. Keep an eye on it: When it looks like all the "repair" that will take place is done, take the top into the house or shop. Place it on several 1"-thick scraps and let it stabilize for a few days. Then finish it and install on the chest.

If that doesn't remove the cup, you can save thickness by ripping the top into narrower pieces, flattening them, and rejointing the edges. Then glue the top back together. The trade-off? You might need to add more stock (width) to replace that lost to the cutting.

For future projects, once you get a glued-up panel flat and sanded, apply finish as soon as possible on all surfaces to better stabilize it. Also, leave it in the shop or a controlled environment until ready to install or deliver to its final destination.