Using dilatometry and small-angle X-ray diffraction, we have studied under bulk conditions the structural changes and elastic response of dioleoyl phosphatidylcholine bilayers to alamethicin. With increasing peptide concentration, we found a progressive thinning of the membrane. However, in contrast to previously published reports, this thinning exhibits exponential behavior. Furthermore, an increase in alamethicin content resulted in an increased lateral area per lipid and a swelling of the multibilayers which can be attributed to a decrease in the bilayer's bending rigidity by similar to 50%. At the same time, hydration and van der Waals forces remained unaffected by the presence of the peptide. Interestingly, all elastic and structural parameters followed the same exponential form found for the membrane thickness, implying a common underlying mechanism for all of these structural parameters. Our results can be understood by introducing an additional entropy term into the free-energy description of peptide incorporation, a term previously not considered. As a result, we have been able to reconcile recent controversies regarding the effect of peptides on membrane thinning.