Thanks to all the responses to my question. You inspired me to go do more research, and this is what I found:
Sanyo Eneloop are widely regarded as the best batteries out there. The ones I bought have been fine so far but I haven't really put them to the test except to accidentally TOTALLY discharge them. I didn't know that was a no-no.
A big lesson was that a good charger/maintainer is as important as the batteries. I got this one as it was highly recommended. It charges, tests, maintains, and "refreshes" batteries. What it won't do is charge a totally dead one.
It has windows that display the status of each battery, which is very useful. I put some old NiMH batteries that had been a total disappointment in this charger and set it to "refresh." On refresh it charges and discharges the battery repeatedly until the amount of charge it accepts stops increasing with each cycle. It took my 5 year old Energizer NiMH batteries from less than 400 mAh capacity (they were rated at 2500) to over 1700 when they finally had had enough. It took 3 days. They are now useful batteries again, though not like new.
This new smart charger won't recognize a battery that puts out less than .1 volt, and I had run mine flat. Fortunately I had the old dumb charger around. I put them in it for 1 minute, which brought them back up enough that the new charger recognized them as batteries.
Bottom line, rechargables are way better than they used to be, and the chargers are better too.