Is the Universe odd?

We investigate the point-parity and mirror-parity handedness of the large angle anisotropy in the cosmic microwave background (CMB). In particular we consider whether the observed low CMB quadrupole could more generally signal odd point-parity, i.e., suppression of even multipoles. Even though this feature is ``visually'' present in most renditions of the WMAP dataset we find that it never supports parity preference beyond the meagre $95%$ confidence level. This is fortunate as point-parity handedness implies almost certainly a high level of galactic contamination. Mirror reflection parity, on the contrary, is related to the emergence of a preferred axis, defining the symmetry plane. We use this technique to make contact with recent claims for an anisotropic Universe, showing that the detected preferred axis is associated with positive (even) mirror parity. This feature may be an important clue in identifying the culprit for this unexpected signal.