alienator said:
Since it only happens when you're on the small cog in back, you should look at your rear derailleur limits. It sounds like your outside limit isn't, uhm, outside enough. It sounds like the limit is set such that the chain is trying to shift up to the next bigger cog.
What he said.
All good suggestions and possibilities, but you want to tick them off in a systematic way – starting with most specific and least expensive.
Cleaning a dirty system is super easy and super cheap. More of a general issue than small cog specific, but something that should be done anyway.
The “H” limit screw is a free fix (or very inexpensive @ LBS) and is almost 100% a small cog related adjustment. If that’s what it is – you’re done.
Barrel adjustment could be needed too, but you can change the indexing interface of all the cogs with that adjustment, so go easy. If your driveline is heavily worn, good chance adjusting the barrel adjuster will throw off the “wear pattern” of the chain and other cogs. You may end up with a smooth running smallest cog and start skipping on the others. If so, smile and take it in stride … it could be time to replace some stuff.
You didn’t say how many miles you have on the existing driveline. If not at least a thousand or more, then you shouldn’t have a lot of wear in the system (unless you’ve let it get gritty). As noted, it isn’t normal for the smallest cog to be most worn, but it can happen if you run that cog often and the chainline has been out of adjustment. On many cassettes the smallest cog is separate – ease of replacement will depend on the cassette you have now. The manufacturer might offer replacement cogs, or you might be able to salvage one from a bike buddy with a parts bin. New cassettes run the gamut - $20 to $200+
If you have the tools to do your own maintenance, it never hurts to have an extra chain or two in your parts bin, a couple of cassettes, and some chainrings. These parts will wear eventually and need to be replaced … just a matter of time. Or take it to your LBS, get professional service and help the cycling economy.