The problem of inherently differing time scales of core and valence electrons in Monte Carlo (MC) simulations is circumvented in a straightforward and intuitive manner. By appropriately subdividing into equivalent subspaces the high-dimensional (many-electron) space in which Monte Carlo integration is done, it is possible to choose completely independent and appropriate sampling times for each "electron." This approach trivially satisfies detailed balance. The partitioning of space is applicable to both variational and Green's function MC. Such a partitioning, however, only provides a significant computational advantage in variational MC. Using this approach we were able to have inner electrons move with reasonably large steps and yet avoid excessive rejection, while outer electrons were moved great distances in few steps. The net result is a large decrease in the sampling autocorrelation time, and a corresponding increase in convergence rate. Results of several standard algorithms are compared with the present acceleration algorithm for the atoms Be and Ne, and the molecule Li-2.