  Galactic nuclei are now generally thought to have density cusps in their
centres, and the evidence is mounting that as a consequence they are unlikely
to be triaxial. Self-consistent stellar dynamical models of non-axisymmetric
cusps would be an interesting counter-argument to this conclusion. We consider
2-d analogues of triaxial cusps: a sequence of non-axisymmetric, cuspy discs
first described by Sridhar & Touma (1997). Scale-free models with potential
{}$\Phi\propto r^\alpha$ are examined in detail. It is shown analytically for
$0<\alpha \la 0.43$ that self-consistent models with positive phase-space
density do not exist. Numerical solutions of the combined Vlasov and Poisson
equations suggest that the whole sequence of models with $0<\alpha<1$ are also
unphysical. Along with existing work on cusps, we conclude on purely
theoretical grounds that galactic nuclei are not expected to be triaxial.
