New terms are proposed for the atomic mass law which incorporate effects of nuclear deformation and shell structure including interference effects between unfilled neutron and proton shells. In addition, a surface-symmetry term is included. Coulomb terms are fixed by recent radii determinations in electron scattering. The standard deviation of calculated masses is reduced by the addition of the new terms as is the error in extrapolating from one side of the valley of beta stability to the other. The usefulness of the law for calculating the mass and binding energy of atoms with large neutron excess is discussed. A table giving mass excess, neutron, proton and alpha-particle binding energies, and beta decay transition energies is appended.