Thanks for the replys, sounds like more info is needed.

Sorry for the laymans terms for this stuff, but Ill try to describe it as
best I can.

So the handle screws onto a stem, and it is the stem itself that rotates to
control the flow of water and appears to be the problem. I of course first
tried to see if just the handles were loose on the stems by tightening the
screw that attaches the handle to the stem, but no luck.

I then removed several handles and wiggled the stems themselves, finding
that they were indeed very loose- i.e. it wouldnt matter how tight the
handle was on, these things are gonna more around. They are loose laterally
by the way.

The stems are made of plastic, as is most of the assembly I can see. It is
pretty bizzare, from what you guys say these things should last a bit longer
than 12 years, but out of 8 handles of the identical make, all 8 are very
lose and wobbly.

Let me know if more info is required!

Cheers,
Bryan