Extensive microscopic molecular dynamics simulations have been performed to study the effects of short-chain alcohols, methanol and ethanol, on two different fully hydrated lipid bilayer systems (POPC and DPPC) in the fluid phase at 323 K. It is found that ethanol has a stronger effect on the structural properties of the membranes. In particular, the bilayers become more fluid and permeable: ethanol molecules are able to penetrate through the membrane in typical timescales of approximately 200 ns, whereas for methanol that timescale is considerably longer, at least of the order of microseconds. A closer examination exposes a number of effects due to ethanol. Hydrogen-bonding analysis reveals that a large fraction of ethanols is involved in hydrogen bonds with lipids. This in turn is intimately coupled to the ordering of hydrocarbon chains: we find that binding to an ethanol decreases the order of the chains. We have also determined the dependence of lipid-chain ordering on ethanol concentration and found that to be nonmonotonous. Overall, we find good agreement with NMR and micropipette studies.