The rate at which coherence is established in an FEL oscillator can be extremely slow. This is particularly true if the electron beam is relativistic such that the electrons and radiation move at nearly the same speed. In this case information about the amplitude and phase of two different portions of the radiation signal is communicated between these points at a slow rate relying on beam slippage. If a low-loss dispersive element is added to the feedback loop the rate at which coherence is established can be greatly enhanced without destroying the tunability of the device. An interesting side effect of the addition of dispersion to the system is the appearance of a modulational instability of the radiation pulse. This instability is similar to the sideband instability in that it causes a monochromatic radiation signal to spontaneously develop sidebands. It is different, however, in that the instability is due to the radiation amplitude dependence of the beam-induced frequency shift as opposed to the amplitude dependence of the gain.