We describe a new layered phase, the discotic smectic, found in Monte Carlo simulations of hard parallelepipeds : This phase differs from the existing smectic A phase in that the shortest particle axis, rather than the longest, is aligned perpendicular to the layers. A range of particle shapes with dimensions varying from 5 X 1 X 1 ("rods") to 5 X 1 X 5 ("tiles") has been studied. We identify the important role played by correlations arising from the stacking of flat surfaces in stabilizing the layered order. We find that 5 X 1 X 1 rods can also exhibit such correlations through orientational disorder. Over this range of particle shapes no nematic phase is observed.