A combined method for the prediction of protein tertiary structures from sequence is presented. This multistep procedure initially uses a simplified approach to protein structure prediction, MONSSTER, that assembles structures from initial extended conformations and scares them. Then, using the lowest-energy low-resolution model as a starting conformation, a detailed atomic model is built and refined using molecular dynamics simulations that employ the locally enhanced sampling (LES) methodology with the particle mesh Ewald (PME) technique for calculation of long-range electrostatic interactions. The combined method is applied to a small disulfide-rich 29-residue protein CMTI-1, a trypsin inhibitor found in squash seeds. Starting with an initial low-resolution model from MONSSTER, which has an rmsd from the native conformation of 3.7 Angstrom (5.0 Angstrom) for C-alpha atoms (all heavy atoms), LES/PME refinement leads to a structure that is only 2.5 Angstrom (3.3 Angstrom) from native, with a C-alpha rmsd of only 1.7 Angstrom for residues 5-29. These rmsd values should be compared to C-alpha rmsd values of 1.2 Angstrom (all residues) or 0.8 Angstrom (residues 5-29) found in PME molecular dynamics simulations that start with the native conformation.