  Cosmological simulations suggest that dark matter haloes are not spherical,
but typically moderately to strongly triaxial systems. We investigate methods
to convert spherical potential-density pairs into axisymmetric ones, in which
the basic characteristics of the density profile (such as the slope at small
and large radii) are retained. We achieve this goal by replacing the spherical
radius r by an oblate radius m in the expression of the gravitational
potential.
  We extend and formalize the approach pioneered by Miyamoto & Nagai (1975) to
be applicable to arbitrary potential-density pairs. Unfortunately, an
asymptotic study demonstrates that, at large radii, such models always show a
R^(-3) disc superposed on a smooth roughly spherical density distribution. As a
result, this recipe cannot be used to construct simple flattened
potential-density pairs for dynamical systems such as dark matter haloes.
Therefore we apply a modification of our original recipe that cures the problem
of the discy behaviour. An asymptotic analysis now shows that the density
distribution has the desired asymptotic behaviour at large radii (if the
density falls less rapidly than r^(-4)). We also show that the flattening
procedure does not alter the shape of the density distribution at small radii:
while the inner density contours are flattened, the slope of the density
profile is unaltered.
  We apply this recipe to construct a set of flattened dark matter haloes based
on the realistic spherical halo models by Dehnen & McLaughlin (2005). This
example illustrates that the method works fine for modest flattening values,
whereas stronger flattening values lead to peanut-shaped density distributions.
