  We present some new results regarding simulations of finite density QCD based
on a canonical approach. A previous study has shown that such simulations are
feasible, at least on small lattices. In the current study, we investigate some
of the issues left open: we study the errors introduced by our approximation of
the action and we show how to tune it to reduce the cost of the simulations
while keeping the errors under control. To further reduce the cost of the
simulations, we check the reliability of reweighting method with respect to the
baryon number. Finally, using these optimizations, we carry out the simulations
at larger densities than in our previous study to look for signals of a phase
transition.
