  We show how to increase the accuracy of estimates of the two-point
correlation function without sacrificing efficiency. We quantify the error of
the pair-counts and of the Landy-Szalay estimator by comparing them with exact
reference values. The standard method, using random point sets, is compared to
geometrically motivated estimators and estimators using quasi-Monte~Carlo
integration. In the standard method, the error scales proportionally to
$1/\sqrt{N_r}$, with $N_r$ being the number of random points. In our improved
methods, the error scales almost proportionally to $1/N_q$, where $N_q$ is the
number of points from a low-discrepancy sequence. We study the run times of the
new estimator in comparison to those of the standard estimator, keeping the
same level of accuracy. For the considered case, we always see a speedup
ranging from 50% up to a factor of several thousand. We also discuss how to
apply these improved estimators to incompletely sampled galaxy catalogues.
