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 } can not be greater than about { \gamma / 2 } .
Discs or bars with a shallow central profile ( \gamma \leq 0.3 ) should not be strongly elliptical .