A generalized multidimensional contact potential is introduced for simulating a simplified model of protein tertiary structure. The contact energy between two residues is a simultaneous function of five interatomic distances, which allows orientational correlations between the backbone and side chains to be represented. The minimization of this potential is enhanced by the use of three levels of coarse-grained potentials as screening functions which can cheaply reject unfavorable structures. The approximate potentials are systematically derived from the full contact potential by averaging over the unwanted degrees of freedom. Results are shown for the minimization of three medium-sized (60-146-residue) proteins and compared with earlier results. The performance of the hierarchical algorithm as a function of the coarse-graining scheme and screening cutoffs is discussed, as well as the dependence of the potential evaluation on system size. The results from the three test proteins show a significant improvement from the NZ scaling observed without the use of the screening potentials.