The temperature dependence of the small-angle neutron scattering from aqueous multilammellar DMPC lipid bilayers, containing small amounts of cholesterol, is analyzed near the main phase transition by means of a simple geometric model which yields the lamellar repeat distance, the hydrophobic thickness of the bilayer, the interlamellar aqueous spacing, as well as fluctuation parameters. The observation of anomalous swelling behavior in the transition region is interpreted as an indication of bilayer softening and thermally reduced bending rigidity. Our results indicate that the effect of small amounts of cholesterol, ≲3 mole%, is a softening of the bilayers in the transition region, whereas cholesterol contents above this range lead to the well-known effect of rigidification. The possible biological relevance of this result is discussed.