The derivation of a Hamiltonian describing the quadrupolar and chemical-shift interactions is presented in terms of irreducible spherical-tenser algebra, Some potential ambiguities concerning the sign of the asymmetry parameters, in this nomenclature, are identified and clarified, A more robust algorithm for handling the boundary conditions imposed by the constraints on asymmetry parameters is described and implemented in a nonlinear-least-squares minimization procedure, In addition, a detailed account is given on a more efficient method for computing the NMR lineshape, and protocols for the extraction of NMR parameters from solid-state lineshapes are introduced. (C) 1995 Academic Press, Inc.