We use models constrained by remotely sensed data from Pine Island and Thwaites Glaciers, West Antarctica, to infer basal properties that are difficult to observe directly. The results indicate strong basal melting in areas upstream of the grounding lines of both glaciers, where the ice flow is fast and the basal shear stress is large. Farther inland, we find that both glaciers have ‘mixed’ bed conditions, with extensive areas of both bedrock and weak till. In particular, there are weak areas along much of Pine Island Glacier’s main trunk that could prove unstable if it retreats past the band of strong bed just above its current grounding line. In agreement with earlier studies, our forward ice-stream model shows a strong sensitivity to small perturbations in the grounding line position. These results also reveal a large sensitivity to the assumed bed (sliding or deforming) model, with non-linear sliding laws producing substantially greater dynamic response than earlier simulations that assume a linear-viscous till rheology. Finally, comparison indicates that our results using a plastic bed are compatible with the limited observational constraints and theoretical work that suggests an upper bound exists on maximum basal shear stress.