katy, it's hard to say exactly without a picture to see what determines the tension and stability.

if it's just a matter of worn threads, you might try some loc-tite instead of glue...loc-tite is what they use on engine bolts they don't want to loosen...it's a chemical that actually melts metal and makes like a plastic weld.

there's another product called JB Weld...it's 2 tubes of a greyish epoxy you mix together 50/50 and does miracles...I use it to patch gas tanks, fix broken speedometer cables, and all sorts of medium duty stress stuff.

if the threads are OK, and the stability is determined by a mating surface "flange" that's rocking, the wobble may be the threaded part itself actually bending and in that case, loc-tite won't mean squat.

can you post a picture so I can see the physical design?
I (we) could likely provide a better answer if i knew what we're talking about for sure.

Katy, I agree with modre about a picture being worth a 1000 words to help you out with this.

One word of caution with any glues, adhesives, expoxies, etc it to make sure that you won't need it to come apart in the future as some of these could result in rather permanent type "fixes". If it needs to come apart then make sure you go for something that isn't labeled as permanent.

Maybe teflon tape, like plumbers use on pipe threads, as you could wrap it to the needed thickness to tighten up the threads without it being permanent?

Post some pics if you can.

David

How about using the next larger metal screw, or if both sides are accessible, a nut and bolt?
Norm

Thanks so much to all of you for helping. I'm going to have DH read these posts to see how he wants to go about fixing the problem.
Katy

If you try the loktite, read the info on the tube to find how much heat it takes to release the loktite. that way if you want to take it apart later, you'll be able to.
Mike A

If the threads are a standard ptch a Helicoil repair kit can be used to restore the worn female threads. The kits come with a drill bit, special STI (Steel Thread Insert) tap, and shapped thread inserts that screw in.