The surface slopes of submarine accretionary wedges generally decrease away from the toe or deformation front toward the arc. This paper presents evidence that this characteristic convex cross-sectional shape is a direct mechanical response to the lithification of sediments during accretion. The recently accreted sediments near the toe, which are typically unconsolidated and therefore very weak, must deform until a critical taper is attained at which they are stable in the presence of the horizontal tectonic compression. This critical wedge taper, and thus the bathymetric slope of the accretionary prism, is relatively high for the porous, weak sediments near the toe. In contrast, the compacted sediments farther back in the wedge are stronger, so they require a relatively modest critical taper and therefore a lower bathymetric slope to be stable under the same tectonic compression. The result is a convex cross-sectional wedge shape. We investigate several possible causes of the increase in cohesive strength with decreasing porosity. A straightforward generalization of the exact critical taper model is combined with empirical cohesion-porosity-velocity relations to infer the distribution of porosity and P wave velocity within the Barbados accretionary wedge. We estimate that the porosity decreases from its near-toe value of 70% to approximately 30% at a depth of 3 km below the seafloor and a distance of 60 km arcward from the front of the wedge.