We develop two new spectral formalisms for the gravitationally self-consistent solution of the ''sea level equation'' which governs the redistribution of glacial meltwater on a visco-elastic Earth. The first is a purely spectral technique based on an extension of theory outlined by Dahlen (1976) for determining the equilibrium oceanic tide on an elastic planet. Using this technique, with a feasible spherical harmonic truncation level (l≤30), we can obtain convergence in the computed sea level variations within the degree range l≤10. We also develop a second, ''pseudospectral'' technique, however, which permits the construction of gravitationally self-consistent solutions to much higher degree and order (l≫100). The pseudospectral formalism is employed here to develop a comprehensive physical explanation for the global pattern of present-day sea level variations due to an ongoing glacial isostatic adjustment. In particular, we focus upon a mechanism, which we term ''equatorial ocean syphoning,'' that acts to draw water toward the oceanic portion of the collapsing peripheral bulge that encircles previously glaciated regions. The collapse of the forebulge induces a flow of water which is required to maintain hydrostatic equilibrium. The syphoning mechanism dominates the relative sea level (RSL) variation in oceans in the far field of the ice sheets (that is, beyond the peripheral bulge) during periods, such as the interglacial of the past 4000 years, during which the volume of the ice sheets has not (apparently) changed appreciably, while, at the same time, isostatic adjustment persists. The RSL change in the near field is, in contrast, dominated by the (local) vertical displacement of the solid surface. Finally, comparison of gravitationally self-consistent predictions of RSL change in the far field, with the observational data at small Pacific island sites, has provided an upper bound of 1 to 2 m for the eustatic sea level rise produced by any recent (last 3000 years) melting of the Antarctic ice sheet. ¿American Geophysical Union 1991