Nanodiscs™ consist of small phospholipid bilayer discs surrounded and stabilized by amphiphilic protein belts. Nanodiscs and their confinement and stabilization of nanometer sized pieces of phospholipid bilayer are highly interesting from a membrane physics point of view. We demonstrate how the detailed structure of Di-Lauroyl-Phosphatidyl Choline (DLPC) nanodiscs may be determined by simultaneous fitting of a structural model to small-angle scattering data from the nanodiscs as investigated in three different contrast situations, respectively two SANS contrasts and one SAXS contrast. The article gives a detailed account of the underlying structural model for the nanodiscs and describe how additional chemical and biophysical information can be incorporated in the model in terms of molecular constraints. We discuss and quantify the contribution from the different elements of the structural model and provide very strong experimental support for the nanodiscs as having an elliptical cross-section and with poly-histidine tags protruding out from the rim of the protein belt. The analysis also provides unprecedented information about the structural conformation of the phospholipids when these are localized in the nanodiscs. The model paves the first part of the way in order to reach our long term goal of using the nanodiscs as a platform for small-angle scattering based structural investigations of membrane proteins in solution.