The well-known model for the critical taper of an accretionary wedge includes overpressure as a first-order parameter. Fluid overpressures reduce frictional resistance at the base of a wedge but they also act as body forces on all material particles of the wedge, in addition to that of gravity. By means of sandbox modeling, many workers have tried to verify the predictions of the critical taper model, but few of them have so far incorporated true fluid pressures. We have used scaled experiments, in which compressed air flows through sand packs, so as to model the deformation of overpressured wedges. A new apparatus provides for a horizontally varying fluid pressure, for example, a linear variation, as in the critical taper model. We have done three series of experiments, involving horizontal shortening of homogeneous or multilayered sand models for various gradients of fluid pressure. As predicted by the critical taper model, the apical angle of the resulting wedge depends on the overpressure gradient. In homogeneous sand at a high overpressure gradient, deformation becomes diffuse and looks ductile. In multilayered models, detachments form beneath layers of low permeability, so that thrusts propagate rapidly toward the undeformed foreland. The efficiency of a detachment and its ability to propagate depend not only on the fluid pressure but also on the permeability ratios between the various layers.