We present a new series of calculations in the theory of spinodal decomposition. The computational scheme is based on a simple ansatz for the two-point distribution function which leads to closure of the hierarchy of equations of motion for the high-order correlation functions. The resulting theory is accurate throughout the spinodal region of the phase diagram, including at the boundaries of this region where the spinodal mechanism is difficult to distinguish from nucleation and growth. The computational scheme is worked out in detail for parameters approximating those of the three-dimensional, kinetic, spin-exchange Ising model with nearest-neighbor interactions. Numerical agreement with recent Monte Carlo data appears to be satisfactory.