For practical problems, efficient but accurate solution methods are usually preferred to computationally expensive but extremely accurate ones. The Muskingum-Cunge (M-C) method is an efficient technique often applied to solve flood routing problems. There are two free parameters in the M-C method: the spatial step and the temporal step. The accuracy of the method wholly depends on the Courant number (essentially the ratio of these step sizes). It is not known which combination of spatial and temporal step yields the best solution. In this study, the concept of column holdup (which is quite often employed in solute transport problems) and the results from the truncation error analysis of the kinematic wave equation are combined to obtain a straightforward condition leading to optimal spatial and temporal steps. It is found that a simple explicit scheme is the best method to solve the complete diffusion wave equation starting from the kinematic wave equation. The scheme attains third-order accuracy if the optimal Courant number is 1/2.