I shall present a new method for solving the Schrödinger equation, numerically exactly, by using a nested contracted basis. Rovibrational wavefunctions are computed in a |v>|JKM> basis, where |v> is a vibrational wavefunction and |JKM> is a symmetric top wavefunction. In turn, the |v> are obtained by solving a vibrational Schrödinger equation with basis functions that are products of contracted bend and stretch functions. The calculations are done in internal coordinates that facilitate the treatment of large amplitude motion. An Eckart molecule-xed frame is used by numerically computing coecients of the kinetic energy operator. The ecacy of the method is demonstrated by calculating a large number of converged J = 10 methane rovibrational levels in the Tetradecad polyad (vibrational energies in the range 5100 - 6100 cm-1). These ideas are used to obtain an accurate methane PES by starting with the ab initio PES of Schwenke and Partridge [Spectrochim. Acta A 57, 887 (2001)] and adjusting ve of their parameters to reproduce 39 reliable vibrational levels of CH4. This reduces the rmsd from 4.3 cm-1 to 0.4 cm-1.