Global Positioning System (GPS)-based receivers appear capable of obtaining Δh, the ellipsoidal height differences, to about 2-4 ppm of the distance separating the end points. The historical record of vertical crustal motion has been obtained from spirit leveling and therefore gives changes in elevation in terms of orthometric height. For GPS-based height differences to be useful in extending the record of height change, the geoid-ellipsoid separation ΔN needs to be evaluated. But is it possible to find ΔN gravimetrically to the precision to which Δh can be measured? This analysis shows that the inner zone contribution to ΔN could be more precise than is Δh from GPS. This contribution to ΔN should be better than ¿ 5 cm over 100 km if the random errors in the 10 km by 10 km mean gravity anomalies do not exceed ¿3 mGal and provided the gravity and elevation data used to obtain the gravity means are connected onto the national gravity and (at last) third-order leveling networks, respectively. For lines of mean elevation greater than 2 km the error in ΔN will exceed specifications unless the density of the subsurface material can be estimated to better than ¿ 200 kg m-3. Results of other tests suggest that the remote zone contribution to ΔN (&psgr;>2.0¿) is adequately represented by high degree (nmax ≂ 180) geopotential models. A small test with the suggested method, performed in the White Sands Test Area, appears to confirm the above data specifications and supports the conclusions of two other investigations that ΔN can be evaluated from gravimetry to precisions which match that of Δh from GPS, at least over shorter lines.