The shock imparted by a laser beam striking a metal surface can be increased by the presence of an optically transparent tamper plate bonded to the surface. We explore the shock produced in an aluminum slab, for a selection of tamper materials and drive conditions. The experiments are conducted with a single-pulse laser of maximum fluence up to 100 J/cm2. The pressure and impulse are measured by photon doppler velocimetry, while plasma imaging is used to provide evidence of nonlinear tamper absorption. We demonstrate a pressure enhancement of 50x using simple commercially available optics. We compare results from hard dielectric glasses such as fused silica to soft plastics such as teflon tape. We discuss the mechanism of pressure saturation observed at high pulse fluence, along with some implications regarding applications. Below saturation, overall dependencies on pulse intensity and material parameters such as mechanical impedances are shown to correlate with a model by Fabbro et al.