My commuter would make a squeaking noise while pressing pedals when the chain was on the either of the two smallest cogs, regardless of the chainring.

At first I thought it was the cassette, also my freehub body was wobbling. I relubed everything I could think of, no change. Eventually I got a second set of wheels for winter riding with studded tires and... same thing: different wheel, different hub and cassette; still squeaking. The chain and cassettes were all new, installed at the same time, no stuck/stiff links. The crankset was used but not worn out.

So I replaced the chain and the squeaking is gone. Why would it happen? Both were Shimano 9-sp chains. The cassettes were Shimano Deore 9sp. I mean the problem is gone but I'm wondering what was wrong.