This paper introduces a technique that reduces the number of state savings and the maximum memory needed for the Time Warp. We present a technique to determine if an event is safe or not. If an event execution is safe, no state saving is carried out. The technique discards some saved states even though the time stamps are larger than the GVT. We prove that the technique is correct under both aggressive and lazy cancellation scheme. This technique can be implemented with minimal additional overhead. Benchmark results on circuit simulation show that the mechanism can reduce the number of state savings and maximum memory size significantly. The technique is applicable to hardware simulation, network simulation and other systems that have fixed interconnection.