Cold, subducted lithosphere has relatively fast seismic velocity which leads to early arrivals for some event-station paths. The effect is very large for events in the Tonga-Kermadec deep seismic zone recorded at certain New Zealand stations. These particular arrivals are very high-frequency (3 Hz or greater) and sometimes resemble two distinct phases, the later arrival appearing at about the time predicted by Jeffreys-Bullen tables. Data from the digital station SNZO in Wellington confirm the travel time results of the analog stations and furthermore show frequencies above 5 Hz, much higher than can be seen on analog records, and up to 4% dispersion in the range 1--8 Hz. Energy in the second phase (which is often absent at SNZO) is mainly 1--2 Hz. The digital data support the idea, proposed earlier, that the effect is caused by propagation through a thin slab which passes only short-wavelength waves. The essential features of the wave propagation are modeled by acoustic waves in a one-dimensional high-velocity slab; the waveforms produced by the model are discussed in terms of the leaky modes of the system and calculated by a reflectivity method. A very thin (<15 km) uniform slab provides the required dispersion, but the waves are heavily attenuated and would never be observed at teleseismic distances; a thicker slab allows the energy through but does not give enough dispersion. Altering the variation of velocity across the slab provides the required dispersion if a thick high-velocity layer, with wave speed increasing gradually with height, is overlain by a thin lid of even higher velocity. For the models considered the lid thickness must lie in the range 6--15 km and be continuous from a depth of about 50 km to the bottom of the earthquake zone. The thick layer could arise from the thermal anomaly in the subducted lithosphere; the thin lid may be the gabbroic part of the subducted crust that has transformed to eclogite. ¿1991 American Geophysical Union