Hey, I just installed a new cassette - a sunrace 7-speed and new 7-speed "Z" chain (kmc) with huge 34t granny cog jump at the bottom of the cassette. I use friction shifters and all the cogs work just fine except the smallest one....which the chain skips over repeatedly.
I have the derailleur high limit dialed in just fine, so I know it's not that the chain is just unable to reach the cog properly. Since I don't ever use an 11t cog on any of my bikes (and only seldom use the 12 or 13), I plan to just dial the high limit to avoid the smallest cog.
What would cause this nonsense? I've gone through 4-5 cassettes on this set-up in the last couple of years and never seen this happen.