I have used the known epicenters and depths of 307 nuclear tests at the Nevada Test Site (NTS) and 75 tests at the East Kazakhstan Test Site to compare the distances between actual and calculated hypocenters (mislocations) with calculated location confidence limits (errors). Each test was located using its ISC-compiled P first arrivals, a starting depth of 33 km and the IASP91 velocity model. I also applied azimuth and incident angle-dependent station corrections to the arrival times. The most accurately located tests are those at the Kazakhstan Test Site, where all of the mislocations in latitude and longitude are less than ±10 km and 90% of the depth mislocations are less than 20 km. Bayesian confidence limits calculated from the least-squares covariance matrix satisfactorily account for these mislocations. At the Nevada Test Site, 90% of the mislocations are less than ±9 km in longitude, ±15 km in latitude, and 33 km in depth. The overestimates in depth are compensated for by origin times that are 2 to 5 sec late. The larger mislocations at NTS occur in spite of the fact that the closest recording sites are less than 200 km away, compared to 1800 km away at the Kazakhstan Test Site. A significant fraction of the depth mislocations at NTS are much larger than their calculated errors. I interpret this failure of the calculated errors to adequately account for the NTS mislocations as being due to systematically late arrivals at northwestern American stations relative to the predicted IASP91 values. By using a locally determined three-layer velocity model for the travel times of phases recorded at distances of less than 1500 km, I was able to reduce 90% of the depth mislocations to less than 11 km as well as significantly reducing the latitude, longitude, and origin time mislocations. I conclude that differences between the IASP91 model and velocities in the vicinity of the explosions may introduce a significant bias into the determined depths of nuclear tests. A similar bias would therefore be expected in the similarly determined depths of shallow earthquakes.