We explore a novel approach to perform decoding-order optimization in the vertical Bell Labs layered space-time (V-BLAST) architecture. Allowing for simultaneous transmission of multiple, separately encoded data streams, the V-BLAST transmit-receive scheme applies to the uplink of a multi-user communication system. A multi-antenna receiver decodes data streams successively, dealing with inter-stream interference by means of cancelling and nulling; interference from previously decoded streams is cancelled by subtraction, and remaining interference is nulled by linear equalization. The order in which the streams are decoded can have a noticeable impact on system performance. We consider the optimization of a fixed decoding order in fast Rayleigh fading, based on long-term channel-fading parameters. For a wide range of performance measures, we show that the fast-fading ordering problem can be treated as a classical linear assignment problem, allowing a solution using existing, efficient algorithms.