Transient dynamic topography is maintained by time-varying density anomalies deep within Earth's mantle. There is considerable interest in predicting and measuring dynamic topography because its spatial and temporal variation will help to track changes in the pattern of mantle convection. Despite the availability of increasingly elaborate predictive models, there is little agreement about the amplitude, wavelength, and rate of change of dynamic topography. Here we analyze a hybrid data set of subsidence observations from continental and oceanic basins in Southeast Asia, where published dynamic models predict 1–2 km of regional subsidence. Residual subsidence was isolated by removing the well-defined effects of lithospheric extension and/or cooling. At long wavelengths (∼103 km), the amplitude of residual subsidence (i.e., maximum permissible dynamic subsidence) has an upper bound of only ∼300 m. The spatial distribution of permissible dynamic topography has no simple spatial or temporal relationship to the pattern of subduction over the past 65 m.y.; anomalous subsidence commenced 5–10 m.y. ago, accelerating to a present-day rate of ∼100 m/m.y. Our results show that density anomalies within the lower mantle have little apparent influence at Earth's surface. Instead, the distribution of residual subsidence reported here can be accounted for by minor variations in lithospheric thickness or by transient density variations beneath the lithospheric plate. The absence of measurable dynamic topography is surprising and indicates that mantle mass anomalies are supported elsewhere, presumably at internal boundaries within Earth. Our hybrid data set can thus be used as an independent constraint on the viscosity structure of the mantle.