There is considerable interest in the credibility of probabilities of exceedance estimated by ground-motion models for very high accelerations. A common statistical approach to this problem has been to examine the upper-tail shape of the distribution of residuals between recorded data and the model for evidence of suppression of high residuals. In this study, a more direct method is suggested, in which the actual number of times given accelerations are exceeded is compared to the expected numbers in strong-motion data sets. The method is illustrated by application to New Zealand and Japan models for peak ground acceleration (PGA). For the Japan model, which is based on a particularly large data set, the ratio of actual to expected number declines in a statistically significant and regular fashion from about 1 at 0.3g to about 0.15 at 1.0g. If these results are indicative of ground-motion models in general, the implications for probabilistic seismic hazard analyses may be far reaching. The method and results have particular importance for the analysis of seismic hazard at sites of critical facilities where strong ground motions with very long return periods may be of interest.