We have investigated the relationship between geoid height and topography for 53 oceanic plateaus and swells to determine the mode of compensation. The ratio of geoid height to topography was obtained from the slope of a best line fit by functional analysis (i.e., nonbiased linear regression), a method that minimizes both geoid height and topography residuals. This method is more appropriate than traditional least squares analysis that minimizes only geoid height residuals, because uncertainties are present in both data types. We find that approximately half of the oceanic and continental plateaus analyzed have low ratios that are consistent with Airy-compensated crustal thickening. The remaining plateaus, however, have higher geoid/topography ratios than predicted by the simple Airy model, and the seismically determined Moho depths beneath some of these features are too shallow for crustal thicknening alone. A two-layer Airy compensation model, composed of thickened crust underlain by an anomalously low density ''mantle root,'' is used to explain these observations. The Walvis Ridge, and the Agulhas, Crozet, and north Kerguelen plateaus have geoid/topography ratios and Moho depths that are consistent with the two-layer Airy model. The proximity of the Agulhas Plateau to a RRR triple junction during its early development, and the excessive volcanism at active spreading ridges that created the Crozet and north Kerguelen plateaus and the Walvis Ridge, may have produced regions of enhanced depletion and hence the low-density mantle anomalies. If this explanation is correct, then the low-density mantle anomaly persists over time and remains embedded in the lithosphere beneath the oceanic feature. ¿ American Geophysical Union 1991