A preliminary one-dimensional velocity model for Mt. Veniaminof, Alaska, was derived by a trial-and-error approach based on a group of 63 volcano-tectonic (VT) earthquakes with magnitudes ranging between 0 and 2.8 and mostly occupying a volume of 140 x 70 x 40 km. We tested 2,164 different velocity models and found that a modified version of the regional velocity model used in routine locations yielded the smallest RMS values of travel times, on average. The epicenters of earthquakes did not vary significantly among all the models tested and we infer that these locations are reasonably well constrained. The focal depths of earthquakes have been constrained to within one kilometer, or less, with the use of Wadati-Riznichenko diagrams. A systematic decrease with depth of the Vp/Vs ratio is apparent in the Mt. Veniaminof area but lateral variations in velocity cannot be resolved with the available data. We found that the hypocenters are located between 0.2 and 50.3 km below sea level and in the upper 20 km they cluster in two regions that diverge from the active vent and enclose a relatively aseismic volume. We found that VT earthquakes are uncommon close to the active vent and within the caldera but persistently occurr off to the sides of the SE-NW alignment of quaternary cones in the Mt. Veniaminof area. This suggests that the active magma system beneath the volcano consists of a dike or system of dikes whose pressure variations cause stresses in the crust and movement along pre-existing faults. From January 2004 until the time of this writing (August 2004) Mt. Veniaminof has had enhanced shallow local seismicity characterized by low-frequency earthquakes and tremor episodes near the vent, each associated with ash-laden puffs that reach a few kilometers above the active cone.