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.

Thanks.