Liquid crystal/polymer dispersions have widely recognized promise as light modulators in projection displays for high definition video. Achieving switching voltages compatible with active matrix display drivers while maintaining good on-screen contrast remains an area of active material research. As the driving voltage depends linearly on the liquid crystal/polymer dispersion thickness, one simple method to lower driving voltage is to operate with thinner dispersions. This approach has a significant impact on contrast ratio. We report on the results of a study of the dependence of the driving voltage and contrast ratio as a function of thickness. For very thin samples the voltage does not decrease with thickness and the contrast is greatly reduced, indicating a clear limit to this approach.