The NP-hard Subset Interconnection Design problem, also known as Minimum Topic-Connected Overlay, is motivated by numerous applications including the design of scalable overlay networks and vacuum systems. It has as input a finite set V and a collection of subsets V 1 , V 2 ,. .. , Vm ⊆ V , and asks for a minimum-cardinality edge set E such that for the graph G = (V, E) all induced subgraphs G[V 1 ], G[V 2 ],. .. , G[Vm] are connected. We study Subset In-terconnection Design in the context of polynomial-time data reduction rules that preserve the possibility to construct optimal solutions. Our contribution is threefold: First, we show the incor-rectness of earlier polynomial-time data reduction rules. Second, we show linear-time solvability in case of a constant number m of subsets, implying fixed-parameter tractability for the parameter m. Third, we provide a fixed-parameter tractability result for small subset sizes and tree-like output graphs. To achieve our results, we elaborate on polynomial-time data reduction rules which also may be of practical use in solving Subset Interconnection Design.