Residual amplitude modulation (RAM) is an unwanted noise source in electro-optic phase modulators. The analysis presented shows that while the magnitude of the RAM produced by a MgO:LiNbO3 modulator increases with intensity, its associated phase becomes less well defined. This combination results in temporal fluctuations in RAM that increase with intensity. This behavior is explained by the presented phenomenological model based on gradually evolving photorefractive scattering centers randomly distributed throughout the optically thick medium. This understanding is exploited to show that RAM can be reduced to below the 105 level by introducing an intense optical beam to erase the photorefractive scatter.