This paper explores the suggestion that observations of large igneous crustal thickness at rifted volcanic margins may in part be explained by small-scale convection in the upper mantle. This may increase the delivery of magma to the overlying lithosphere without the need for anomalously high mantle temperatures. This concept is quantitatively assessed by numerical modeling of the flow, caused by divergent plate motions, in a viscous, temperature- and pressure-dependent, nonlinear fluid. Significant time-dependent small-scale convection is generated at the lower model viscosities (and/or higher temperatures, and/or sharper rift geometries). These models can provide the required thick igneous crust observed at volcanic margins. However, they also give excessive variations in the thickness of igneous crust within the ocean basin and are therefore unacceptable. An additional factor we have explored is the recent suggestion that the oceanic mantle may become dehydrated when melt is generated and removed. This increases its viscosity by 2 to 3 orders of magnitude in the melting zone, above ~80 km. The high-viscosity lid stabilizes the flow and provides a more uniform oceanic crustal thickness, while at the same time allowing for vigorous small-scale convection during the early history of the rift and the delivery of thick igneous crust against the margin. This factor, coupled to the models for flow described above, allow the main features of volcanic margins to be simulated. Besides the thick igneous crust predicted at the margins, these models suggest that time-dependent small-scale convection below the margin may persist for tens of million years following the onset of seafloor spreading and that there may be coupling between this flow at the margin and that at the ridge axis. The periodicity of this time-dependent convection is primarily dictated by the model viscosities; the models suggest that episodicities of tens of million years are reasonable. These episodicities may be reflected in the record of vertical motions at rifted margins. ¿ 1999 American Geophysical Union