Evolutionary convergence is often appealed to in support of claims about multiple realization. The idea is that convergence shows that the same function can be realized by different kinds of structures. I argue here that the nature of convergence is more complicated than it might appear at first look. Broad claims about convergence are made by biologists during general discussions of the mechanisms of evolution. In their specialized work, though, biologists are often more limited in the claims they make. I (...) will examine a standard example to show how claims about convergence can be oversimplified. (shrink)