The power of three-dimensional orientation detection of single emitting dipoles using a sophisticated scheme with three detectors in a confocal microscope is quantitatively explored by means of Monte Carlo simulations. We show that several hundreds of photons are sufficient for a reliable orientation determination. In typical single-molecule experiments, time resolutions in the submillisecond range for orientation trajectories become accessible. Experimental data on fluorescent latex beads and single perylene monoimide molecules show that a properly aligned setup can perfectly reproduce the simulated data. The simulations and experimental data highlight the potential of our method and give practical guidelines for its application.