Computational prediction of membrane permeability to small molecules requires accurate description of both the thermodynamics and kinetics underlying translocation across the lipid bilayer. In this contribution, well-converged, microsecond-long free-energy calculations are combined with a recently developed subdiffusive kinetics framework to describe the membrane permeation of a homologous series of short-tail alcohols, from methanol to 1-butanol, with unprecedented fidelity to the underlying molecular models. While the free-energy profiles exhibit barriers for passage through the center of the bilayer in all cases, the height of these barriers decreases with the length of the aliphatic chain of the alcohol, in quantitative agreement with experimentally determined differential solvation free energies in water and oil. A unique aspect of the subdiffusive model employed herein, which was developed in a previous article, is the determination of a position-dependent fractional order which quantifies the degree to which the motion of the alcohol deviates from classical diffusion along the thickness of the membrane. In the aqueous medium far from the bilayer, this quantity approaches 1.0, the asymptotic limit for purely classical diffusion, whereas it dips below 0.75 near the center of the membrane irrespective of the permeant. Remarkably, the fractional diffusivity near the center of membrane, where its influence on the permeability is the greatest, is similar among the four permeants despite the large difference in molecular weight and lipophilicity between methanol and 1-butanol. The relative permeabilities, which are estimated from the free-energy and fractional diffusivity profiles, are therefore determined predominantly by differences in the former rather than the latter. The predicted relative permeabilities are highly correlated with existing experimental results, albeit they do not agree quantitatively with them. On the other hand, quite unexpectedly, the reported experimental values for the short-tail alcohols are nearly three orders of magnitude lower than the available experimental measurement for water. Plausible explanations for this apparent disagreement between theory and experiment are considered in detail.