Why is deciding simulation preorder (and simulation equivalence) computationally harder than deciding bisimulation equivalence on almost all known classes of processes? We try to answer this question by describing two general methods that can be used to construct direct one-to-one polynomial-time reductions from bisimulation equivalence tosimulation preorder (and simulation equivalence). These methods can be applied to many classes of finitely generated transition systems, provided that they satisfy certain abstractly formulated conditions. Roughly speaking, our first method works for all classes of systems that can test for `non-enabledness' of actions, while our second method works for all classes of systems that are closed under synchronization.