  We present an efficient method for building equilibrium multi-component
galaxies with non-spherical haloes and bulges. The gist of our approach is to
tailor the velocity ellipsoid directly to the geometry of the mass
distribution. Thus we avoid computing the anisotropic velocity dispersions
which leads to large savings in the cpu budget. The computational time of the
algorithm for triaxial equilibria scales linearly with the number of particles,
N. The approximate solution to the velocity field causes structural relaxation:
tests with N = 50,000 show that fluctuations of the inertia tensor (not
exceeding the 10 per cent level) disappear within one half of a revolution at
the half-mass radius. At later times equilibrium properties settle to values
close to those sought from the initial conditions.
  A disc component is then added as described by Hernquist (1993).
Incorporating the above algorithm to his code BuildGal, test runs show that the
stability of the disc against vertical heating is not substantially modified by
using our method.
  The code, MaGali, is made generally available.
