We present an algorithm for reducing the number of continuous states of a discrete time linear switched system, such that the reduced system has the same input-output behavior as the original system for a subset of switching sequences. The procedure can be interpreted as reachability and observability reduction for a linear switched system with constrained switching. The proposed method is expected to be useful for abstraction based control synthesis methods for hybrid systems. (C) 2016 Elsevier Ltd. All rights reserved.