Using velocity profiles from sites in Japan, California, Turkey, and Europe, we find that the time-averaged shear-wave velocity to 30 m (V_S30), used as a proxy for site amplification in recent ground-motion prediction equations (GMPEs) and building codes, is strongly correlated with average velocities to depths less than 30 m (V_Sz, with z being the averaging depth). The correlations for sites in Japan (corresponding to the KiK-net network) show that V_Sz is systematically larger for a given V_Sz than for profiles from the other regions. The difference largely results from the placement of the KiK-net station locations on rock and rocklike sites, whereas stations in the other regions are generally placed in urban areas underlain by sediments. Using the KiK-net velocity profiles, we provide equations relating V_S30 to V_Sz for z ranging from 5 to 29 m in 1-m increments. These equations (and those for California velocity profiles given in Boore, 2004b) can be used to estimate V_S30 from V_Sz for sites in which velocity profiles do not extend to 30 m. The scatter of the residuals decreases with depth, but, even for an averaging depth of 5 m, a variation in logV_S30 of ±1 standard deviation maps into less than a 20% uncertainty in ground motions given by recent GMPEs at short periods. The sensitivity of the ground motions to V_S30 uncertainty is considerably larger at long periods (but is less than a factor of 1.2 for averaging depths greater than about 20 m). We also find that V_S30 is correlated with V_Sz for z as great as 400 m for sites of the KiK-net network, providing some justification for using V_S30 as a site-response variable for predicting ground motions at periods for which the wavelengths far exceed 30 m.