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'To take full advantage of the parallelism in a standard multigrid algorithm requires as many processors as points. However, since coarse grids contain fewer points, most processors are idle during the coarse grid iterations. Frederickson and McBryan claim that retaining all points on all grid levels (using all pro-cessors) can lead to a 'superconvergent ' algorithm. Has the 'parallel supercon-vergent ' multigrid algorithm, PSMG, of Frederickson and McBryan solved the problem of implementing multigrid on a massively parallel SIMD architecture? How much can be gained by retaining all points on all grid levels, keeping all processors busy? The purpose of this work is to show that the PSMG algorithm, though it achieves perfect processor utilization, is no more efficient than a parallel imple-mentation of standard multigrid methods. PSMG is simply a new and perhaps M& simpler way of achieving the same results. '4