Well, it will shift to a higher gear, but it takes two clicks of the shifter and it skips over a gear when it does shift. With one click the chain hangs on the current gear by the slimmest if threads. It's quite amazing really.
This is a new derailleur, a Shimano RD-M410 Alivio SGS, on a cog set that predates index shifting. Could that be the problem?
I have tried adjusting the barrel adjuster, but that doesn't seem to have any effect (on this problem).
Also, I put bar-end shifters on the bike, so the cable seems a bit short.
The cog set has 7 gears, but the shifter has 8.