  We present a general scheme for constructing Monte Carlo realizations of
equilibrium, collisionless galaxy models with known distribution function (DF)
f_0. Our method uses importance sampling to find the sampling DF f_s that
minimizes the mean-square formal errors in a given set of projections of the DF
f_0. The result is a multi-mass N-body realization of the galaxy model in which
``interesting'' regions of phase-space are densely populated by lots of
low-mass particles, increasing the effective N there, and less interesting
regions by fewer, higher-mass particles.
  As a simple application, we consider the case of minimizing the shot noise in
estimates of the acceleration field for an N-body model of a spherical
Hernquist model. Models constructed using our scheme easily yield a factor ~100
reduction in the variance in the central acceleration field when compared to a
traditional equal-mass model with the same number of particles. When evolving
both models with a real N-body code, the diffusion coefficients in our model
are reduced by a similar factor. Therefore, for certain types of problems, our
scheme is a practical method for reducing the two-body relaxation effects,
thereby bringing the N-body simulations closer to the collisionless ideal.
