A soluble theory of the post‐saturation portion of a beam‐plasma interaction is developed, concentrating on explaining the results of O’Neil, Winfrey, and Malmberg. Analytic progress is made possible by applying a certain constraint procedure, characterized by the ’’rotating‐bar’’ approximation, to a Hamiltonian formulation of the problem. The procedure yields, from the originalN‐particle HamiltonianH, a new, reduced Hamiltonian H˜, which has only two particle‐related degrees of freedom, and which maintains the conservation laws of energy and momentum possessed byH. The equations of motion coming from H˜ still describe the self‐consistent interaction of a mode of the plasma with the beam particles, as opposed to previous work, and, because of the great reduction in the number of degrees of freedom, explicit expressions for the nonlinear frequency shift, and growth rate, of the mode can be obtained, which are in very good agreement with the simulation results of O’Neil, Winfrey, and Malmberg.