We introduce an iterative scheme to solve the drift-diffusion device simulation problem, which combines the Gummel iteration with the “pointwise iteration”, and then we compare its convergence behavior with other iteration strategies, for different test cases. Comparisons are made with the standard Gummel approach and a nonlinear multigrid iteration. The combined “Gummel-Pointwise” iteration has significantly better convergence characteristics than the Gummel iteration in all cases. The cost of the pointwise iteration varies only linearly with the number of grid points. While in terms of CPU time for the solution the pointwise iteration is not always faster in 2-D, in 3-D the combined technique becomes more and more advantageous as the grid size increases. It is found that the nonlinear multigrid scheme is overall not as effective as the combined iteration.