Monte Carlo simulations of proteins are hindered by the system’s high density which often makes local moves ineffective. Here we devise and test a set of long range moves that work well even when all sites in a lattice simulation are filled. We demonstrate that for a 27-mer cube, the ground state of random heteropolymers can quickly be reached. We discuss results for 48-mer systems where the ground state is known exactly. For ten sequences that were examined, the introduction of long range moves speeds up the search for the ground state by about one order of magnitude. The method is compared to a fast folding chain growth algorithm that had previously been used with much success. The new algorithm here appears to be more efficient. The point is illustrated by the folding of an 80-mer four-helix bundle considered previously.