The predictability of seismic signals from nearby traces can be a powerful tool for reducing random or locally coherent noise. The choice of algorithm to reduce noise for a given application is a function of the data signal and noise characteristics. When the signal and noise are relatively consistent over a given design window, an f-x domain Wiener-filter approach can be used. For cases in which the data are time- or space-varying, a new approach using 2-D adaptive filtering in the t-x domain can be very effective. In either of these approaches, a prediction trace-gap can often be successfully used to remove locally coherent noise when lateral signal changes are not too rapid.