We study models of concurrency based on labelled transition systems where abstractions are induced by a partition of the action set. We introduce dimming relations which are able to relate two models if they can mimic each other by using actions from the same partition block. Moreover, we discuss the necessary requirements for guaranteeing compositional verification. We show how our new relations and results can be exploited when seemingly heterogeneous systems exhibit analogous behaviours manifested via different actions. Dimming relations make the models more homogeneous by collapsing such distinct actions into the same partition block. With our examples, we show how these abstractions may considerably reduce the state-space size, in some cases from exponential to polynomial complexity.