The rate-distortion problem for two-layer coding of a pair $(X,Y)$ of correlated sources is considered. The first layer information enables reconstruction of $X$ within a certain distortion $D_X$, while reception of both layers additionally enables reconstruction of $Y$ within distortion $D_Y$. While this problem is a special case of the successive refinement problem, the computation of the rate-distortion region for this scenario is non-trivial. Using a general class of outer bounds to the successive refinement rate-distortion region, the successive coding rate-distortion region for the case where $(X,Y)$ is a jointly Gaussian pair and the distortion measure is squared error is explicitly characterized.