In this study, we consider wide-sense nonblocking operation of a converting-space-converting switching fabric. We propose a routing strategy based on the functional decomposition of second-stage switches, called the XsVarSWITCH routing strategy. This routing strategy is suitable for all kinds of three-stage switching fabrics operating in a slotted mode, regardless of frequency, time, or other types. We consider in this study a three-stage switching fabric. The first and third stages comprise switches with converting capability, while the middle stage is composed of space switches. The proposed routing strategy can reduce the number of required center-stage switches by almost 94% in some cases, as compared to the number of middle-stage switches under strict-sense nonblocking conditions.