We approach the controversial anomalous swelling problem in membrane systems using small angle neutron scattering to measure relative changes in the bilayer thickness of unilamellar vesicles of dimyristoylphosphatidylcholine lipid bilayers in the vicinity of the main transition. These measurements conclusively demonstrate that at least half of the anomalous swelling previously observed in multilamellar vesicles of this system can be accounted for by the critical thickening of the bilayer itself, in contrast to conclusions drawn from several recent studies.