Path-based methods for the determination of nondispersive drainage directions in grid-based digital elevation models are presented. These methods extend the descriptive capabilities of the classical D8 method by cumulating the deviations between selected and theoretical drainage directions along the drainage paths. It is shown that either angular or transversal deviations can be employed. Accordingly, two classes of methods designated D8-LAD (eight drainage directions, least angular deviation) and D8-LTD (eight drainage directions, least transversal deviation) are developed. Detailed tests on four synthetic drainage systems of known geometry and on the Liro catchment (central Italian Alps) indicate that the proposed methods provide significant improvement over the D8 method for the determination of drainage directions and drainage areas.