I study a simple variation of the algorithm of Metropolis et al. for simulating statistical systems. The trial changes in any given variable are taken from a region of phase space far from the old value but involving only small changes in energy. This results in correlation times which are short compared to the usual applications of the algorithm of Metropolis et al. Tests with SU(2) and SU(3) lattice gauge theories indicate substantial possible savings in computation time relative to standard approaches.