Geochemical models of melting at mid-ocean ridges-particularly those based on trace elements and uranium-decay-series isotopes-predict that melt segregates from the matrix at very low porosities, of order 0.1%. Some of these models also require that the melt ascends rapidly. But these predictions appear to conflict with seismic data obtained by the mantle electromagnetic and tomography (MELT) experiment. These data reveal, beneath the East Pacific Rise (at 17 degrees S), a region of low velocities several hundred kilometres wide, which is best explained by the presence of 1-2% melt, distributed on a grain scale in disk-shaped geometries. Here I show that these apparently contradictory constraints can be reconciled by taking into account the geometry and resulting permeability of the intergranular network of melt, together with the changing character of the melt as it ascends. A deep, volatile-rich melt with low viscosity and density is mobile at 0.1% porosity, but basaltic melt only becomes mobile at a porosity above 1%. While the volumetric contribution of the volatile-rich melt to the erupted basalts is small, the isotopic disequilibria (except for radium) generated by porous flow of this melt are preserved if melt transport is rapid at the onset of high-productivity melting. Also, because of incomplete extraction, some melt is retained in a broad zone, consistent with the MELT observations.