A method for varying the wavelength of a free electron laser (FEL) by applying an energy dither to the charged particles supplying the FEL. Bunches of charged particle beams are accelerated by cavities that are operated at a harmonic of the bunch repetition rate. The method involves adding one or more secondary radiofrequency accelerator cavities after the primary beam transport and near the wiggler to apply a fluctuation between individual bunches with a pseudo-random distribution. The secondary radiofrequency accelerator cavities provide fine variations of the beam energy about a nominal operating point. Operating a free electron laser (FEL) with a 1% change in the electron beam energy via the added secondary cavities will result in a 2% wavelength variation of the FEL output.