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Standard sequential time marching schemes limit parallelism to the spacial domain. With computer architectures growing in size rather than clock speeds, additional speed-up must come from greater parallelism. We propose a multigrid reduction method that incorporates temporal parallelism into general time-stepping routines, allowing for dramatic speed-ups on large architectures. For a nonlinear equation, each iteration of the parallel-in-time method requires an expensive, nonlinear, spatial solve. Using a simple nonlinear equation, with a Picard method as the nonlinear solver, we investigate several methods for reducing the computational cost of this spatial solve, including reducing solver accuracy on coarser levels and introducing spatial coarsening.