The lamellar orientation in supported, thin films of poly(styrene-b-butadiene) (P(S-b-B)) depends on block copolymer molar mass. We have studied films from nine block copolymer samples with molar masses between 13.9 and 183 kg/mol using grazing-incidence small-angle X-ray scattering (GISAXS) and have found that in low molar mass samples the lamellae are parallel to the substrate surface, whereas they are perpendicular for high molar masses. For a thick, high molar mass film, the bulk limit is approached; i.e., randomly oriented lamellae are present. The 2D GISAXS images are discussed quantitatively in the framework of our recently developed distorted-wave Born approximation model (Busch, P.; et al. J. Appl. Crystallogr. 2006, 39, 433). The results cannot be explained from enthalpic considerations alone but point to the importance of entropic factors.