  The shape of a cusped galactic nucleus is constrained by the range of shapes
of orbits in its gravitational potential. It is shown for scale-free
non-axisymmetric discs that while a plausible elongated density model requires
at least some orbits to spend more time near the major axis than anywhere else,
both regular boxlets and tube orbits generally cross the major axis too fast
for self-consistency. If galaxies host inner nuclear discs or flat bars with a
cuspy surface light profile ($\gamma=|{d \log \mu / d \log r}|>0$), their
ellipticity $1-{b / a}$ cannot be greater than about ${\gamma / 2}$. Discs or
bars with a shallow central profile ($\gamma \le 0.3$) should not be strongly
elliptical.
