Thanks everyone!
Mrrabbitt, I'm glad to hear it's not a bad rim. While I'm going to sell the bike, I still have something of a sentimental attachment to it and I didn't want to put something too junky on it. At the same time, it's not a particularly valuable bike that would justify putting a lot of money into it. It's a 1984 Schwinn Le Tour Luxe. It was my first decent bike, but I just don't use it anymore.