  When starting an N-body simulation of an isolated galaxy, it is desirable to
select particles from a distribution function to ensure that the model is in
equilibrium. Random sampling from a DF is widely used, but results in a set of
particles that differs by shot noise from that intended. This paper presents a
method to reduce sampling noise that has been developed by the author in a many
collaborations over a number of years. The technique has been partly described
in past papers, though the ideas have not previously been gathered together,
nor have its advantages been clearly demonstrated in past work. Of course,
sampling errors can also be reduced by a brute force increase in the number of
particles, but methods to achieve the same effect with fewer particles have
obvious advantages. Here we not only describe the method, but also present
three sets of simulations to illustrate the practical advantages of reducing
sampling error. The improvements are not dramatic, but are clearly worth
having.
