The evolution of thin foils accelerated over distances much greater than their in-flight thickness has been studied for a classical, low power density regime (5 × 1012 and 2 × 1013 W/cm2 at λ = 1.054 μm, 0.15 THz bandwidth). Two illumination modes have been used, one of these being based on a near-field, multi-lens array ISI smoothing, the other on focusing by F/1 aspherical lenses. The results seem to be encouraging with regard to the possibility of getting smooth, spatially uniform acceleration over distances of the order of 100 × IFFT (In-Flight-Foil Thickness). The experiments with nonsmoothed beams have shown a sort of refractive interchange stabilization for the initial on-target imprinting of the illumination non-uniformities.