What is considered "instability" by some might be called "nimble" or "agile" to others. Stability is more about the rider than the bike, and after enough miles, even the twitchiest bike will become easier to handle. I've mentioned it before in other threads, but if you really want to improve your stability and pedaling technique, spend some time on rollers. I had ridden for years before I acquired a set of rollers which someone had thoughtfully left on a curb on trash day. I rescued them out of curiosity, and spent a couple hours learning how to balance on them. When I took my bike out on the road after that couple hours, the improvement in my stability was astonishing. I hate using trainers, and rollers aren't any more fun, but nothing is better for improving your balance and stability on a bike.