Small-angle neutron scattering (SANS) experiments were performed on unilamellar 1,2-dimyristoylphosphatidylcholine (DMPC) vesicles prepared in heavy water by extrusion through polycarbonate filters with 500 A pores. The data obtained at 30+/-0.1 degrees C were evaluated using a five-strip function model of the bilayer coherent neutron scattering length density, three different approximate form factors describing scattering from vesicles, and different methods of evaluation of the experimental data. It is shown that the results obtained from the SANS data in the range of scattering vector values 0.0316 A(-1)< q<0.0775 A(-1) are not sensitive to the vesicle form factor, nor to the evaluation method. Using the hollow sphere model of vesicles convoluted with the Gaussian distribution of their sizes, a constrained bilayer polar region thickness of 9 A and a DMPC headgroup volume of 325.5 A(3), it was possible to obtain from the experimental data the DMPC surface area as 58.9+/-0.8 A(2), the bilayer thickness as 44.5+/-0.3 A and the number of water molecules as 6.8+/-0.2 per DMPC located in the bilayer polar region.