The discrete ordinates method, the leading method of deterministic neutron transport calculations, can generate efficient numerical solutions to problems of interest in reactor physics. In criticality problems, numerical solution requires two levels of iteration: outer and inner iterations. For loosely coupled nuclear systems, the dominance ratio is close to unity and the outer iterations are hampered by slow rates of convergence. Inner iterations can become exceedingly slow if the system is characterized by a large scattering to total cross section ratio. In this work, the coarse mesh rebalance and diffusion synthetic acceleration techniques have been applied to both outer and inner iterations in spherical geometry multigroup discrete ordinates calculations. Using numerical experiments, the relative merits of both suggested acceleration methods are assessed.