Thin films of cylinder-forming polystyrene-poly(n-hexyl methacrylate) diblock copolymers, PS-PHMA, are attractive as nanolithographic templates, an application which demands good control over the thin-film structure-yet the quality of order achieved to date in PS-PHMA films has fallen short of this ideal. In the present work, a series of PS-PHMA diblocks of varying composition, all forming PS cylinders, are synthesized and their morphology studied as a function of film thickness in both nonsheared and shear-aligned films. In nonsheared films, the cylinder axis orientation relative to the surface switches from parallel to perpendicular as a function of film thickness; this oscillation is damped out as the fraction of the cylinder-forming block (PS) increases, away from the sphere-cylinder phase boundary. In aligned films, thicknesses which possess the highest coverage of parallel cylinders prior to shear show the highest quality of alignment postshear, as measured by the in-plane orientational order parameter of the cylinder axis. In well-aligned samples of optimal thickness, the quality of alignment is limited by isolated dislocations, whose density is highest at high PS contents, and by undulations in the cylinders' trajectories, whose impact is most severe at low PS contents; consequently, polymers whose compositions lie in the middle of the cylinder-forming region exhibit the highest quality of alignment.