A generalized random-phase approximation (RPA) for decoupling the double-time Green's functions (DTGF) equations of motion of spin systems is developed. The decoupling parameters are chosen by fixing the moments of both the commutator and anticommutator decoupled spectral functions, thus establishing a well-defined relationship between the approximation scheme and the fundamental properties of DTGF. It is shown that the standard RPA must be supplemented by a condition on correlations to provide a well-defined, complete approximation scheme. The procedure is demonstrated by application to the fully anisotropic S=1/2 Heisenberg model in a field.