Numerical evaluation of the steady-state neutron flux distribution in a slightly subcritical nuclear reactor due to the presence of a fixed external source is considered by using neutron diffusion theory. It has been shown in the literature that in the particular case when keff is very close to unity (say, within 1 mk), many solution techniques face severe convergence problems. In this context, an acceleration method called Accelerated SubCritical Multiplication (ASCM), originally suggested in the well-known neutron transport code TORT, is investigated in this paper specifically for such cases. The studies are based on a realistic heavy water reactor test case analyzed by two-group diffusion theory. ASCM is found to work very well. It is useful even when the distributions of the external source and the fission source are vastly different. ASCM is based on iterative scaling of the overall flux level in the reactor. An alternative way to evaluate the “scaling factor” is discussed. A somewhat new ASCM-like scheme is suggested to accelerate the Jacobi and Gauss-Seidel iterations needed for the within-group calculations. Conditions for the effectiveness of this scheme are discussed. Implications of the present work in reactor kinetics and some other fields are indicated.