Signi.cant advances have been made in heuristic search for classical planning in the last six years. Most of these planners use A* style search. We report on two sound and complete domain-independent classical planners AWA* (Adjusted Weighted A*) and MAWA* (Modified AWA*) in this paper. AWA* is the .rst planner to use node-dependent weighting in A*. MAWA* uses a two-phase heuristic evaluation. MAWA* applies node-dependent weighting to a subset of the nodes in the fringe, after the two-phase evaluation. We report on an empirical comparison of AWA*, MAWA* with classical planners AltAlt, FF and STAN 4. Both AWA* and MAWA* outperform AltAlt and STAN 4. Both AWA* and MAWA* solve many problems that FF does not. The ideas in AWA* and MAWA* are general enough to be applicable in solving other planning problems like temporal planning and planning with resources and numerical variables.