Neuroprosthetic devices such as a computer cursor can be controlled by the activity of cortical neurons when an appropriate algorithm is used to decode motor intention. Algorithms which have been proposed for this purpose range from the simple population vector algorithm (PVA) and optimal linear estimator (OLE) to various versions of Bayesian decoders. Although Bayesian decoders typically provide the most accurate off-line reconstructions, it is not known which model assumptions in these algorithms are critical for improving decoding performance. Furthermore, it is not necessarily true that improvements (or deficits) in off-line reconstruction will translate into improvements (or deficits) in on-line control, as the subject might compensate for the specifics of the decoder in use at the time. Here we show that by comparing the performance of nine decoders, assumptions about uniformly distributed preferred directions and the way the cursor trajectories are smoothed have the most impact on decoder performance in off-line reconstruction, while assumptions about tuning curve linearity and spike count variance play relatively minor roles. In on-line control, subjects compensate for directional biases caused by non-uniformly distributed preferred directions, leaving cursor smoothing differences as the largest single algorithmic difference driving decoder performance.