I have no idea if this works, but it's something to read about.

http://firmatop.com/Firmatop/Welcome.html

I put a cheap memory foam mattress underneath my expensive memory foam mattress, not to give "support", but to add volume. It does prevent bottoming out.

If it's an inner spring mattress there may be no help. A bad bouncy mattress won't ever give you good sleep. You might try putting the mattress on a platform and using it as a box spring for a good firm futon.

Thanks for the suggestions. I think I'm going to try plywood under the mattress as a first step. I think adding a topper will give more volume but not enough support. I looked at the link above and they charge $200 but more important, they have no twin size options. Thanks again everyone.

My mother developed a bad back and needed an extra firm mattress, so she added plywood and it seemed to do the trick.

If you just bought the mattresses, I would see if you can exchange them. Most mattress places let you exchange them within some period of time for a modest restocking fee.