We propose a stochastic method to reduce the autocorrelation time of a general Monte Carlo (MC) method and apply it to the variational quantum Monte Carlo (VMC) simulation of full-core atoms. We achieve a reduction in autocorrelation time of at least a factor of four compared with the standard method. Further, we find an approximate analytic fit to our results which gives a comparable reduction in autocorrelation time at essentially no cost. Our analytic form is independent of the geometry of the system being modeled and, therefore, can be easily applied to the VMC simulation of solids; it may also prove useful in any MC simulation where there are widely varying length scales. Results are presented for C, F, and Si.