Time and offset varying velocity filtering can be achieved by limiting the data input to forward tau-p transforms. This limiting procedure, called hyperbolic velocity filtering (HVF), suppresses transform-related artifacts as well as coherent and noncoherent noise while retaining elliptical (reflection) events. We show that HVF can be viewed as a muting process in the slant-stack domain. Based on this simple but physical interpretation of HVF, a more efficient computer implementation is proposed. We further examine possible applications for HVF for processing seismic reflection data and illustrate the results using both synthetic and real data examples.