Accuracy in measuring displacement in optical interferometers is limited by cyclic errors introduced by various leakage paths within the system. Existing techniques to reduce this nonlinearity do not work when there is large optical loss in the target path, such as for long-range measurements. We describe a new approach to reducing nonlinearity that overcomes these limitations. Based on phase modulation of the laser light, and requiring minimal additional components, experiments have demonstrated rejection of the effects of leakage in the presence of large optical loss.