We describe the design and characterization of a compact dual-polarization lidar that uses a liquid crystal variable retarder (LCVR) to discriminate between backscattered polarization states on alternate laser pulses (at 30 Hz). Measurements of the polarization discrimination of the system, including the liquid crystal and a Schmidt-Cassegrain receiver telescope, show that depolarization ratios can be determined with an additive error of less than 0.4%. The source is a Nd:YAG laser with a wavelength of 532 nm, pulse energy of 118 mJ, and pulse-repetition frequency of 30 Hz. The normal operating range is 15 km, with a 1.5-m range resolution. The full-angle receiver field of view is variable up to 8.8 mrad. Sample data from atmospheric clouds demonstrate the use of lidar depolarization measurements for distinguishing between ice and liquid water in thin clouds with low multiple scattering (with cloud phase verified using radiosonde profiles of atmospheric temperature and humidity). Also shown is a lidar observation of a depolarizing layer over Bozeman, Montana, identified as subvisual cirrus, aerosols transported from in or near China, or a combination thereof.