Spatial multiplexing, or BLAST, is a signaling technique for multiple-input multiple-output (MIMO) channels in which multiple independent data streams are transmitted in parallel in space. The independence between streams, unfortunately, limits the diversity advantage. In this paper we present a space-time code design, using the linear dispersion code framework, for MIMO Rayleigh fading channels. Our design provides codes that have the same ergodic capacity performance as spatial multiplexing but allows for improved diversity advantage. We present a technique for finding good codes based on successive projection. Monte Carlo simulations illustrate performance improvements over spatial multiplexing in terms of bit error probability.