We present rotation-vibrational levels of water up to the dissociation limit using two recent, global potential energy surfaces. These calculations are performed using our recently developed discrete variable representation (DVR) based parallel code (PDVR3D), which runs on computers with massively parallel processors. Variational tests on the convergence of these results show convergence within 0.5 cm(-1). Analysis of the highest wave functions for the vibrational energy levels are also shown. Tests on previous calculations performed using conventional computers suggest that convergence for high-lying rotationally excited states is not as good as claimed.