  Molecular line lists, particularly those computed for high temperature
applications, often have very few states assigned local quantum numbers. These
are often important components for accurately determining line shape parameters
required for radiative transfer simulations. The projection of the total
angular momentum onto the molecule fixed axis ($k$) is investigated in the
Radau internal coordinate system to determine when it can be considered a good
quantum number. In such a coordinate system, when the square of the $k^{th}$
component of the wavefunction is greater than one half, then we can classify
$k$ as a good quantum number in accordance with the theorem of Hose and Taylor.
Furthermore, it is demonstrated that when this holds true, oblate and prolate
quantum labels $K_{a}$ and $K_{c}$ can reliably be predicted. This is
demonstrated for the water and ozone molecules.
