A systematic approach is given for symbolically caching intermediate results useful for deriving incremental programs from non-incremental programs. We exploit a number of program analysis and transformation techniques, centered around effective caching based on its utilization in deriving incremental programs, in order to increase the degree of incrementality not otherwise achievable by using only the return values of programs that are of direct interest. Our method can be applied straightforwardly to provide a systematic approach to program improvement via caching.