We propose a compression of the opposite-spin coupled cluster doubles amplitudes of the form τijab≡UiaVTVWUjbW, where UiaV are the nV-highest magnitude eigenvectors of the MP2 or MP3 doubles amplitudes. Together with a corresponding parameterization of the opposite-spin coupled cluster Lagrange multipliers of the form λabij≡UiaVLVWUjbW, this yields a fully self-consistent parameterization of reduced-rank coupled cluster equations in terms of the Lagrangian L0TVW,LVW. Making this Lagrangian stationary with respect to the LVW parameters yields a perfectly determined set of equations for the TVW equations and coupled cluster energy. These equations can be solved using a Lyapunov equation for the first-order amplitude updates. We test this “rank-reduced coupled cluster” method for coupled cluster singles and doubles in medium sized molecules and find that substantial compression of the T^2 amplitudes is possible with acceptable accuracy.