We consider the problem of estimating the p-quantile of a distribution when observations from that distribution are generated from a simulation model. The standard estimator takes the p-quantile of the empirical distribution of independent observations obtained by Monte Carlo. As an improvement, we use conditional Monte Carlo to obtain a smoother estimate of the distribution function, and we combine this with randomized quasi-Monte Carlo to further reduce the variance. The result is a much more accurate quantile estimator, whose mean square error can converge even faster than the canonical rate of O(1/n).