The recently introduced GRid-INdependent Descriptors (GRIND) were designed to provide a suitable description of a series of ligands for 3D-QSAR studies not requiring the spatial superimposition of their structures. Despite the proven usefulness of the method, it was recognized that the original GRIND failed to describe appropriately the shape of the ligand molecules, which in some cases plays a major role in ligand-receptor binding. For this reason, the original descriptors have been enhanced with the addition of a molecular shape description based on the local curvature of the molecular surface. The integration of this description into the GRIND allows the generation of 3D-QSAR models able to identify both favorable and unfavorable shape complementarity in a simple and alignment-independent way. The usefulness of the new GRIND-shape description in 3D-QSAR is illustrated using two structure-activity studies: one performed on a set of xanthine-like antagonists of the A(1) adenosine receptor; another performed on a series of Plasmodium falciparum plasmepsin II inhibitors.