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 ~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.