The transient, nonlinear Richards' equation describing flow in partially saturated porous media is solved numerically using several time-discretization strategies. The aim of the research is to compare the computational efficiency of conventional iterative schemes with several newer non-iterative formulations. The Implicit Factored method in particular appears to be an attractive alternative because of its high accuracy and two-level nature. The performance of the different schemes is evaluated over a range of accuracy levels, using both the standard form of Richards' equation and a modified form with a forcing term added (allowing comparisons with an exact solution). The limitations and advantages of the different time-discretization approaches are discussed.