We suggest and test potentials for the modeling of protein structure on coarse lattices. The coarser the lattice, the more complete and faster is the exploration of the conformational space of a molecule. However, there are inevitable energy errors in lattice modeling caused by distortions in distances between interacting residues; the coarser the lattice, the larger are the energy errors. It is generally believed that an improvement in the accuracy of lattice modelling can be achieved only by reducing the lattice spacing. We reduce the errors on coarse lattices with lattice-adapted potentials. Two methods are used: in the first approach, 'lattice-derived' potentials are obtained directly from a database of lattice models of protein structure; in the second approach, we derive 'lattice-adjusted' potentials using our previously developed method of statistical adjustment of the 'off-lattice' energy functions for lattices. The derivation of off-lattice Calpha atom-based distance-dependent pairwise potentials has been reported previously. The accuracy of 'lattice-derived', 'lattice-adjusted' and 'off-lattice' potentials is estimated in threading tests. It is shown that 'lattice-derived' and 'lattice-adjusted' potentials give virtually the same accuracy and ensure reasonable protein fold recognition on the coarsest considered lattice (spacing 3.8 A), however, the 'off-lattice' potentials, which efficiently recognize off-lattice folds, do not work on this lattice, mainly because of the errors in short-range interactions between neighboring residues.