Alcouffe’s diffusion-synthetic acceleration scheme for one-dimensional discrete ordinates calculations is extended to accelerate both the zero’th and first moments of the scattering source. The extended scheme is found to be significantly more effective than the standard scheme for problems with highly forward-peaked scattering. A new diffusion theory is derived directly from the discrete ordinates equations, which varies from the standard theory only in the definition of the diffusion coefficient. When employed in the standard diffusion-synthetic acceleration scheme, the new theory is found to perform slightly better than the standard diffusion theory.