Although sterols constitute one of the most important molecular species in cells, the reasons for their structure-function relationships in lipid membranes are not well understood. The main objective of this work is to elucidate the recently suggested possibility that the ordering and condensing effects of sterols on phospholipid membranes are related to the smoothness of a sterol. We focus on cholesterol, which has two methyl groups attached to its beta-face, and compare its properties to those of demethylated cholesterol (Dchol), from which the two methyl groups have been removed. Atomic-scale molecular dynamics simulations of lipid membranes comprised of saturated lipids and sterols, either cholesterol or Dchol, provide compelling evidence that despite its smoother structure, the ordering and condensing effects of Dchol are less effective than those of cholesterol. The ordering capability of both cholesterol and Dchol is highly asymmetric with respect to their ring structure, but whereas cholesterol favors the alpha-face, Dchol favors the beta-face. The origin and implications of this difference are analyzed in detail. The picture that emerges from this study supports a view that the two methyl groups at the steroid ring system of cholesterol play an important role in cholesterol-lipid interactions by reducing sterol tilt in the bilayer and hence allowing for an optimal orientation for cholesterol.