High-quality ship soundings obtained since 1967 in French Polynesia are used to better define the pattern of depth anomalies in French Polynesia and to test the accuracy of previous results based on ETOPO5 gridded data. The modes of the differences between the ship data and ETOPO5 demonstrate that the latter database is accurate to +/-250 m for nearly 70% of the observations in the region, although there is a tendency for ETOPO5 to be of the order of 35 m too shallow. The ship depth versus age distribution shows that the South Pacific's unusually shallow seafloor, termed the ``Superswell,'' cannot simply be described as the cooling of a hotter or thinner thermal plate. Rather, the seafloor rises between the ages of ~40 and 80 million years before resuming thermal subsidence. The Superswell appears to be bounded to the north by the Marquesas Fracture Zone, and the depth anomaly tapers down to smaller values south of the Austral Fracture Zone. Its modal-depth-versus-age relation cannot be mimicked easily by classical steady state thermal cooling models, leading us to prefer dynamic explanations for the depth anomaly. Modal depth analysis aids in the isolation of the individual swells superimposed on the Superswell. Whereas the Marquesas swell, just north of the Superswell, is similar to other swells worldwide in its width (>1000 km) and amplitude (~1 km), both the Society and Austral swells are narrower and lower than global norms. We explain the small size of the Society and Austral swells as the reduced thermal buoyancy of these hotspots entrained in a broader mantle upwelling.