The hierarchical expansion of the kinetic energy (HEKE) operator in curvilinear coordinates presented recently (Strobusch and Scheurer, J. Chem. Phys. 2011a, 135, 124102; Strobusch and Scheurer, J. Chem. Phys. 2011b, 135, 144101) relies on a many-body expansion of the metric tensor. It is shown how this expansion can be adapted to a specific system. An analytic formula is derived, which yields an estimate of the impact of a certain expansion term on the spectrum. In combination with the hierarchical structure of the many-body expansion and interpolation techniques, the memory consumption and evaluation time of the HEKE operator as well as the computational costs for subsequent vibrational self-consistent field and vibrational configuration interaction calculations are reduced significantly, which is demonstrated by studies on two small test systems H2O2 and formaldehyde (H2CO). © 2013 Wiley Periodicals, Inc.