A hypercube with extra connections added between pairs of nodes through otherwise unused links is investigated. The extra connections are made in a way that maximizes the improvement of the performance measure of interest under various traffic distributions. The resulting hypercube, called the enhanced hypercube, requires a simple routing algorithm and is guaranteed not to create any traffic-congested points or links. The enhanced hypercube achieves noticeable improvement in diameter, mean internode distance, and traffic density, and it also is more cost effective than a regular hypercube. An efficient broadcast algorithm that can considerably speed up the broadcast process in enhanced hypercubes is provided. >