  The coherent potential approximation (CPA) is extended to describe
satisfactorily the motion of particles in a random potential which is spatially
correlated and smoothly varying. In contrast to existing cluster-CPA methods,
the present scheme preserves the simplicity of the conventional CPA in using a
single self-energy function. Its accuracy is checked by a comparison with the
exact moments of the Green's function, and with the spectral function from
numerical simulations. The scheme is applied to excitonic absorption spectra in
different spatial dimensions.
