  Improvements beyond the primitive approximation in the path integral Monte
Carlo method are explored both in a model problem and in real systems. Two
different strategies are studied: the Richardson extrapolation on top of the
path integral Monte Carlo data and the Takahashi-Imada action. The Richardson
extrapolation, mainly combined with the primitive action, always reduces the
number-of-beads dependence, helps in determining the approach to the dominant
power law behavior, and all without additional computational cost. The
Takahashi-Imada action has been tested in two hard-core interacting quantum
liquids at low temperature. The results obtained show that the fourth-order
behavior near the asymptote is conserved, and that the use of this improved
action reduces the computing time with respect to the primitive approximation.
