We present optimized implementations of the weak-coupling continuous-time Monte Carlo method defined for nonequilibrium problems on the Keldysh contour. We describe and compare two methods of preparing the system before beginning the real-time calculation: the “interaction quench” and the “voltage quench,” which are found to be suitable for large and small voltage biases, respectively. We also discuss technical optimizations which increase the efficiency of the real-time measurements. The methods allow the accurate simulation of transport through quantum dots over wider interaction ranges and longer times than have heretofore been possible. The current-voltage characteristics of the particle-hole symmetric Anderson-impurity model is presented for interactions up to ten times the intrinsic level width . We compare the Monte Carlo results to fourth-order perturbation theory, finding that perturbation theory is accurate up to or for a voltage bias . The interplay of voltage and temperature and the Coulomb blockade conductance regime are studied.