This paper presents a compositional minimization approach with efficient state space reductions for verifying non-trivial asynchronous designs. These reductions can result in a reduced model that contains the exact same set of observably equivalent behavior in the original model, therefore no false counter-examples result from the verification of the reduced model. This approach allows designs that cannot be handled monolithically or with partial-order reduction to be verified without difficulty. The experimental results show significant scale-up of the compositional minimization approach using these reductions on a number of large asynchronous designs.