Small-angle scattering has been employed to study the structure of lipid bilayers in unilamellar vesicles. This paper evaluates the use of a model approach for the analysis of such data. A long molecular dynamics simulation of a dipalmitoylphosphatidylcholine bilayer in the L(alpha) phase provides detailed structural information from which scattering length density profiles and scattering intensity are obtained. A sequence of increasingly realistic models are defined and then fit to the simulated scattering intensity data for values of q that are experimentally accessible. The models are evaluated by how well they fit the intensity data and the structural parameters of the simulation. Although the conventional approach that extracts only the radius of gyration from a Kratky-Porod plot provides a reasonable fit to much of the data, the available experimental q range supports refined models with two independent parameters. Of the many two-parameter models, we propose that particular choices should be inspired by the functional form of the scattering length density profile of simulations. Constraints that limit realistic models to two independent parameters are described in detail. The analysis supports the proposition that reliable results for area/lipid and hydrocarbon thickness can be obtained from small-angle neutron scattering of unilamellar vesicles.