Two methods to combine fluorescence correlation spectroscopy (FCS) with modulated excitation, in a way that allows extraction of correlation data for all correlation times have been developed and experimentally verified. One method extracts distortion-free correlation data from measurements acquired with standard hardware correlators provided the fluorescence does not change systematically within the excitation pulses. This restriction does not apply to the second method, which, however, requires time-resolved acquisition of the fluorescence intensity. Modulation of the excitation in an FCS experiment is demonstrated to suppress triplet population buildup more efficiently than a corresponding reduction in continuous wave excitation intensity (shown for the dye rhodamine 6G in aqueous solution). Excitation modulation thus offers an additional means to optimize the FCS measurement conditions with respect to the photophysical properties of the dyes used. This possibility to suppress photoinduced states also provides a useful tool to distinguish additional processes occurring in the same time regime in the FCS measurements, as demonstrated here for the protonation kinetics of fluorescein at different pH. In general, the proposed concept opens for FCS measurements with a complete correlation timescale in a range of applications where a modulated excitation is either necessary or brings specific advantages.