We demonstrate that the recently proposed pruned-enriched Rosenbluth method (PERM) (Grassberger, Phys. Rev. E 56:3682, 1997) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare it to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and thus allows one to analyze thermodynamic aspects of the folding behavior of arbitrary sequences.