By limiting data input to the forward-inverse tau-p transform pair, velocity filtering which varies with time and offset can be achieved. The limiting procedure, called hyperbolic velocity filtering, suppresses coherent noise while retaining reflection events. It is based on knowledge of the stacking velocities, but only approximate values are needed. A suitable application for hyperbolic velocity filtering is in hard water-bottom marine areas where laterally propagating noise, diffracted by shallow scatterers, gives rise to reflection-like events with high apparent velocity in the CMP gathers. Such diffractions do not, however, generally have reflection-like moveouts in shot or receiver gathers. Hyperbolic velocity filtering offers moveout discrimination at all offset distances and traveltimes. When it is applied to shot (and receiver) gathers from a hard water-bottom area such as offshore Florida, a striking reduction of noise occurs in the stacked section. Comparison with similar application of fixed-limit (f-k) velocity filtering shows the hyperbolic filtering to be more effective for this data set.