Scalable networks with very good topological properties are often impossible to build because of their prohibitively high wiring complexity. Such a network is the generalized hypercube (GH). It supports full-connectivity of all its nodes in each dimension and is characterized by outstanding topological properties. We propose a new class of scalable interprocessor connections, namely HOWs (Highly-Overlapping Windows), capable of lower complexity than GHs and comparable performance. HOWs are obtained from GHs by removing edges to produce systems of lower wiring complexity. They contain numerous highly-overlapping GHs of smaller size. The classical GH belongs to this new class of interconnections. We demonstrate that 2-D HOWs perform much better than binary hypercubes for important communications patterns.