In those cases where a direct diagonalization of the energy matrix is not attempted because of insuperable practical difficulties of computation, it is always possible to estimate the gamut of the eigenvalue spectrum by a variational method. A trial state function similar in some respects to a Glauber state is employed. Certain asymptotically exact results due to Tavis and Cummings (1968) are recovered. Finally, ways in which the accuracy might be improved are outlined.