In this pedagogical paper, material already in the Jahn–Teller literature is recast in a way that emphasizes how vibronic wavefunctions for the XY 3 Jahn–Teller problem can conveniently be calculated using electronic and vibrational basis set functions that do not transform into their negatives upon going once around the conical intersection and do transform as irreducible representations of the ordinary C 3 v point group. We give as an explicit example, a recalculation of the pseudorotational energy levels and wavefunctions near the bottom of a deep Jahn–Teller moat that does not make use of half-integral quantum numbers. A brief discussion, also recast somewhat from material in the literature, is given of how the basis functions used here are related to the more frequently discussed electronic and vibrational basis functions for the Jahn–Teller problem, which transform into their negatives upon going once around the conical intersection.