Function specialization is a compilation technique that consists in optimizing the body of a function for specific values of an argument. Different versions of a function are created to deal with the most frequent values of the arguments, as well as the default case. Compilers can do a better optimization with the knowledge of run-time behaviour of the program. Static compilers, however, can hardly predict the exact value/behaviour of arguments, and even profiling collected during previous runs is never guaranteed to capture future behaviour. We propose a dynamic function specialization technique, that captures the actual values of arguments during execution of the program and, when profitable, creates specialized versions and include them at runtime. Our approach relies on dynamic binary rewriting. We present the principles and implementation details of our technique, analyze sources of overhead, and present our results.