Molecular structures can be extracted from solution scattering analyses of multidomain or oligomeric proteins by a new method of constrained automated scattering curve fits. Scattering curves are calculated using a procedure tested by comparisons of crystal structures with experimental X-ray and neutron data. The domains or subunits in the protein of interest are all represented by atomic coordinates in order to provide initial constraints. From this starting model, hundreds or thousands of different possible structures are computed, from each of which a scattering curve is computed. Each model is assessed for steric overlap, radii of gyration and R-factors in order to leave a small family of good fit models that corresponds to the molecular structure of interest. This method avoids the tedium of curve fitting by hand and error limits on the ensuing models can be described. For single multidomain proteins, the key constraint is the correct stereochemical connections between the domains in all the models. Successful applications to determine structures are summarised for the Fab and Fc fragments in immunoglobulin G, the three domain pairs in the Fc subunit of immunoglobulin E and the seven domains in carcinoembryonic antigen. For oligomeric proteins, the key constraint is provided by symmetry and successful analyses were performed for the association of the monomers of the bacterial amide sensor protein AmiC to form trimers and pentameric serum amyloid P component to form decameric structures. The successful analysis of the heterodimeric complex of tissue factor and factor VIIa required the use of constraints provided from biochemical data. The outcome of these analyses is critically appraised, in particular the biological significance of structures determined by these solution scattering curve fits.