Loose keywork is a given on any older instrument that has been regularly played, (largely due to metal loss from wear) and the fix is a simple one: about half an hour of swedging and countersinking will bring the mechanism back to near factory snugness.
Ironically, although the procedure is straightforward and the tools inexpensive, I see a lot of rebuilt horns with loose keys. Even when the pad-work is well done, time and effort is largely thrown away due to noise, lost motion, and inconsistent pad seating. To simply clean and replace pads as though it were a modern student horn compromises the functionality of the instrument and wastes the time and money of its owner, as well as perpetuating the illusion that older horns simply can't compare to modern instruments in terms of playability. Here is the fix, in a nutshell:
Often, gaps are small, but even a significant amount of end-wear can generally be remedied by this method. It also helps minimize the wear that takes place inside the tube, bringing it back snug around the rod and thus minimizing play in two dimensions.
As with swedging, this remedies both end- and side- play, stabilizing the key in two dimensions. Countersinks come in a variety of sizes and it is only necessary to measure the head of the screw to choose the correct one for the task. Then, a few twists in the hole, a test with the key, repeat on the other post, and you're done! Always do both posts, to avoid removing too much material from one and leaving the next tech nowhere to go...I try to think of the future when I work on a horn, having been the recipient of so much poor work in my time.
Most older instruments only need a combination of the 2 treatments on a few, heavily used keys. But some clarinets, either more worn or with more generous manufacturing tolerances, require that the work be executed on most keys. It sounds onerous, but half an hour to forty five minutes is the maximum that I generally have to invest, unless I'm dealing with a really old horn, or one with an unusually complex mechanism (such as a Full Boehm).
When both are done properly, the difference is like night and day: Tight, smooth, quiet keys, with pads that seat accurately every time! When next you consider an overhaul for your clarinet or sax, ask the tech if all needed swedging and countersinking is included in the estimate. If he says 'No', or looks confused, take your horn and get the heck out of there! You'll be glad you did...