In current ground-motion models, the uncertainty in predicted ground motion is usually modeled with a lognormal distribution. One consequence of this is that predicted ground motions do not have an upper limit. In reality, however, there probably exist physical conditions that limit the ground motion. Applying the usual uncertainty distribution in probabilistic seismic hazard analysis may lead to groundmotion estimates that are unrealistically large, especially at the low annual probabilities considered for important structures, such as dams or nuclear reactors. A recently proposed statistical procedure to compare the actual and expected numbers of predicted spectral accelerations exceeding a given value gives clear results when applied to a ground-motion model developed for Japan from a very large strong-motion data set. It shows that, for increasingly large spectral accelerations, the actual number of exceedances becomes progressively less than the expected number of exceedances. The pattern of this discrepancy depends on the site class and the earthquake tectonic category. These results suggest that assuming a normal distribution for the prediction errors of an attenuation model (empirical ground-motion prediction equation) is likely to result in overestimation of the extreme values of spectral accelerations.