At many subduction zones, accretionary complexes form as sediments are offscraped from the subducting plate. Existing mechanical models that treat accretionary complexes as critically tapered wedges of sediment demonstrate that pore pressure controls their taper angle by modifying rock strength. We combine a model of groundwater flow with critical-taper theory to show that permeability and plate-convergence rate are important controls on accretionary wedge geometry through their influence on pore pressure. Low permeability and rapid convergence sustain nearly undrained conditions and shallowly tapered geometry, whereas high permeability and slow convergence result in steep geometry. Our results are generally in good agreement with data from active accretionary complexes, but also illustrate the importance of other factors, such as incoming sediment thickness and stratigraphy. One key implication is that strain rate and hydrologic properties may strongly influence the strength of the crust in a variety of geologic settings.