The standard neutral diffusion model is improved by treating the first flight neutrals, originating at the boundary, separately and exactly, and using the diffusion approximation only for the neutrals suffering one or more charge exchange interactions. Different source neutral energies are thereby accommodated unlike the diffusion model which cannot distinguish between bulk plasma neutrals and recycling neutrals. Both models have been implemented in the 2D NEWEDGE code and results for 5 and 50 eV neutrals are contrasted with diffusion model predictions. Significant differences are seen in the divertor plasma density, temperature and heat flux profiles, with the 50 eV neutral energy case showing most dramatic differences. An improvement in convergence rate of the edge plasma code is also seen for the first flight corrected diffusion model.