Systems and methods that enable LED drivers to generate drive signals by implementing a modulation technique referred to herein as “stochastic frequency pulse modulation” (SFPM) are disclosed. The SFPM is based on randomly increasing or decreasing, during every cycle of a drive signal, the amount of time the drive signal is high or low, tracking the deviation of the total amount of time (i.e., for multiple cycles) that the drive signal is high or low from what it should be to provide to a LED a target average power dictated by a target dimming level, and using the tracking to set limits of ranges from which the durations of the time periods when the drive signal is high or low may be randomly selected.