The electric-field-induced structural rearrangement of smectic layers in the antiferroelectric and ferroelectric phases of three different materials is reported. The materials all have high optical tilt angles (around 30 degrees ), compared with the steric tilt angles deduced from layer spacing measurements (around 18 degrees ). The chevron angles observed in devices agree well with values found for the steric tilt angle across the tilted mesophase range. Electric fields were applied to liquid crystal devices while the smectic layer structures, in both the depth and in the plane of the device, were probed using small angle x-ray scattering. Two separate aspects of the influence of the field on the layer structure were studied. First, the organization of the smectic layers in the antiferroelectric phase is described before, during, and after the application of an electric field of sufficient magnitude to induce a chevron to bookshelf transition. Second, the evolution of the field-induced layer structure change has been investigated as the field was incrementally increased in both the antiferroelectric and ferroelectric phases. It was found that the chevron to bookshelf transition has a distinct threshold in the antiferroelectric phase, but shows low or zero threshold behavior in the ferroelectric phase for all the materials studied.