A grooming switch comprises plural input ports for receiving multi-time-slot input signals and plural output ports for forwarding multi-time-slot output signals. At least five switching stages alternate between time switching and space switching. The first stage is connected to the input ports, and the last stage is connected to the output ports. Each intermediate stage is connected to two other stages. Collectively, these stages perform compact superconcentration of the input signals, copying and distribution of the compact superconcentrated signals, and unicast switching of the distributed signals to form the output signals, resulting in a grooming switch that is rearrangeably non-blocking for arbitrary multicast traffic.