  We construct phase-space distribution functions for the oblate, cuspy mass
models of Sridhar & Touma, which may contain a central point mass (black hole)
and have potentials of St\"ackel form in parabolic coordinates. The density in
the ST models is proportional to a power $r^{-\gamma}$ of the radius, with
$0<\gamma<1$. We derive distribution functions $f(E, L_z)$ for the scale-free
ST models (no black hole) using a power series of the energy $E$ and the
component $L_z$ of the angular momentum parallel to the symmetry axis. We use
the contour integral method of Hunter & Qian to construct $f(E, L_z)$ for ST
models with central black holes, and employ the scheme introduced by Dejonghe &
de Zeeuw to derive more general distribution functions which depend on $E$,
$L_z$ and the exact third integral $I_3$. We find that self-consistent two- and
three-integral distribution functions exist for all values $0 < \gamma < 1$.
