Through control of the temperature, T, and film thickness, h, the relative influence of forces associated with crystallization, long-range van der Waals forces, and block-copolymer ordering were manipulated to control the structure of films of asymmetric polyethylene-b-poly(styrene-r-ethylene-rbutene) (E-b-SEB) diblock copolymers. The bulk equilibrium structure of this copolymer consists of spheres of the crystallizable E block embedded in the amorphous SEB matrix. In thin films, the E component resides at the free surface and the SEB block resides in contact with the substrate. Within the temperature range T > T-m, where Tm is the melting temperature, yet below the order-disorder transition (ODT) temperature, T-ODT, all films of thickness h > 12 nm were ordered throughout. The thickness of the brush layer L-0, in contact with the substrate, of these films was 12 nm; this thickness is about one-half of the intersphere spacing of the bulk copolymer. Films equal to or thinner than 12 nm dewet, forming droplets on the substrate. However, at temperatures below the melting temperature but above the glass transition temperature of the amorphous block, films in the same thickness range (h <= 12 nm) were structurally stable. While thicker films were stable as well, crystallization had a significant effect on the topography of these films, particularly as the film thickness increased.