Symmetry reduction methods exploit symmetry in a system in order to efficiently verify its temporal properties. Two problems may prevent the use of symmetry reduction in practice: (1) the property to be checked may distinguish symmetric states and hence not be preserved by the symmetry, and (2) the system may exhibit little or no symmetry. In this paper, we present a general framework that addresses both of these problems.We introduce “Guarded Annotated Quotient Structures” for compactly representing the state space of systems even when those are asymmetric. We then present algorithms for checking any temporal property on such representations, including non-symmetric properties.