We have carried out a detailed investigation of the acceptor tunneling in the water dimer.. This motion is responsible for the largest splitting of vibrational states in the dimer, the so-called acceptor splitting. Our results confirm that this splitting is due to a coupled 2-fold motion: The internal rotation of the donor with respect to the O-O axis, and the wagging of the acceptor. The minimum potential energy path along the corresponding coordinate was computed using the coupled-cluster ab initio with single, double, and perturbative triple excitations (CCSD(T)) method and the augmented correlation consistent polarized valence quadruple basis set (aug-cc-pVQZ). The pure acceptor tunneling energy levels were obtained by the variational method with a free rotor basis. The acceptor splittings associated with the O-H stretching overtone states of the water dimer were calculated with a simple model which employs adiabatic separation between the tunneling motion and high-frequency vibrations.