  We construct simple triaxial generalisations of Navarro-Frenk-White haloes.
The models have elementary gravitational potentials, together with a density
that is cusped like 1/r at small radii and falls off like 1/r^3 at large radii.
The ellipticity varies with radius in a manner that can be tailored to the
user's specification. The closed periodic orbits in the planes perpendicular to
the short and long axes of the model are well-described by epicyclic theory,
and can be used as building blocks for long-lived discs. As an application, we
carry out the simulations of thin discs of satellites in triaxial dark halo
potentials. This is motivated by the recent claims of an extended, thin disc of
satellites around the M31 galaxy with a vertical rms scatter of ~12 kpc and a
radial extent of ~ 300 kpc (Ibata et al. 2013). We show that a thin satellite
disc can persist over cosmological times if and only if it lies in the planes
perpendicular to the long or short axis of a triaxial halo, or in the
equatorial or polar planes of a spheroidal halo. In any other orientation, then
the disc thickness doubles on ~5 Gyr timescales and so must have been born with
an implausibly small vertical scaleheight.
