The optical beam diagnostics at the BESSY II light source in Berlin have been improved significantly over the last few years. In particular, the streak-camera system has been extended in precision and sensitivity to allow two-dimensional imaging in time and space for equilibrated and non-equilibrated bunch patterns. In this paper, we prove experimentally and theoretically that we have reached a sub-ps RMS total time resolution using filtered synchrotron light. Detailed simulations, including the different physical time-dispersion mechanisms, show the influence of various band-pass and edge wavelength filters on the resolution. The limits for unfiltered near-visible synchrotron radiation (white-light) and the band-pass filter to achieve optimal time resolution are derived as well, providing a basis for more advanced beam-dynamics studies in the near future.