Thanks, everyone.
I went to the local Performance shop today and got the Mirricyle mirror--only $12.99--and it seems far superior to the more expensive Blackburn one that it's replacing. I decided I'm really more comfortable with the mirror attached to my bike rather than to my glasses or helmet.
The mounting system on the Mirricyle mirror is much more secure--I don't think it'll go flying off the bike unexpectedly while I'm riding like the other one did--but I'm really wowed by the much greater visibility and adjustability.
The Blackburn one had to be readjusted constantly and was hard to get just right, and this one seems as if it will stay put. I'm very pleased with it, after a five-mile test cruise around the neighborhood.
I also got a Cateye Mity 8 computer, $19.99 I think, and it does everything I need. And if it makes a noise, I can't hear it!