We present the view that for systematic software reuse (SSR) to happen we need a reuse software architecture (RSA) as the invariant base and a collection of reuse software components (RSCs) as the pluggable variant part of a family of architecturally similar software systems. We shall identify a reuse situation with a RSA, RSCs and a plugging operator. SSR is then presented as a case of plugging a collection of RSCs into the appropriate RSA. We apply this view of reuse to a number of reuse cases and find evidence that for reuse to be successful we need simple, clear and easily pluggable RSAs and RSCs.