Further results on combustion of sandwiches made of alternating layers of ammonium perchlorate (AP) and a matrix of AP particles in polymeric binder in an expanded pressure range of 0.345-13.78 MPa (50-2000 psig), over a wide range of matrix lamina thicknesses, are reported. Inclusion of a nanoparticle-size burning rale catalyst in the matrix is also considered. The sandwich burning rates indicate plateaus over the 6.89-13.78 MPa (1000-2000 psig) pressure range for select ranges of matrix lamina thickness. These are correlated with similar plateau trends in the burning rates of composite propellant formulations with bimodal particle size distribution of the oxidizer and appropriate choice of coarse AP size, wherein the fine AP/binder matrices are of identical composition to those tested in the sandwiches. The dependence of the sandwich burning rates on the matrix lamina thickness and the quenched surface features are examined to explain the plateau burning rate trends. The results indicate that the two-dimensional coupling of heat feedback from the hot. near-surface parts of the oxidizer/fuel diffusion flamelets is diminished at elevated pressures due to their greater proximity to the burning surface and the corresponding shrinking of their lateral extent.