We present a novel technique that speeds up state-space exploration (SSE) for evolving programs with dynamically allocated data. SSE is the essence of explicit-state model checking and an increasingly popular method for automating test generation. Traditional, non-incremental SSE takes one version of a program and systematically explores the states reachable during the program's executions to find property violations. Incremental SSE considers several versions that arise during program evolution: reusing the results of SSE for one version can speed up SSE for the next version, since state spaces of consecutive program versions can have significant similarities. We have implemented our technique in two model checkers: Java PathFinder and the J-Sim state-space explorer. The experimental results on 24 program evolutions and exploration changes show that for non-initial runs our technique speeds up SSE in 22 cases from 6.43% to 68.62% (with median of 42.29%) and slows down SSE in only two cases for -4.71% and -4.81%.