We propose a sampling scheme to reduce the CPU time for Monte Carlo simulations of atomic systems. Our method is based on the separation of the potential energy into parts that are expected to vary at different rates as a function of coordinates. We perform n moves that are accepted or rejected according to the rapidly varying part of the potential, and the resulting configuration is accepted or rejected according to the slowly varying part. We test our method on a Lennard-Jones system. We show that use of our method leads to significant savings in CPU time. We also show that for moderate system sizes the scaling of CPU time with system size can be improved (for n=40 the scaling is predominantly linear up to 1000 particles).