The mean dynamic topography of the surface of the ocean is estimated using a finite difference inverse model of the ocean circulation constrained by a prior TOPEX/Poseidon-EGM96 estimate and an ocean density climatology. The EGM96 geoid uncertainties are represented by their full covariance matrix. The model finds a solution that yields a new 1°-resolution dynamic topography estimate with a 5 cm precision. The existence of this solution suggests that the uncertainties in EGM96, despite being much smaller than in previous geopotential models, are nonetheless realistic. The geodetic information constrains the inverse estimate of the ocean circulation, particularly at high latitudes.