Annealing procedures that greatly reduce linear birefringence in single-mode fiber coils are described. These procedures have been successfully applied to coils ranging from 5 mm to 10 cm in diameter and up to 200 or more turns. They involve temperature cycles that last 3-4 days and reach maximum temperatures of about 850 degrees C. The residual birefringence and induced loss, are minimized by proper selection of fiber. The primary application of these coils is optical fiber current sensors, where they yield small sensors that are more stable than those achieved by other techniques. A current sensor with a temperature stability of +8.4*10/sup -5//K over the range from -75 to +145 degrees C has been demonstrated. This is approximately 20% greater than the temperature dependence of the Verdet constant. Packaging degrades the stability, but a packaged sensor coil with a temperature stability of about +1.6+10/sup -4//K over the range from -20 to +120 degrees C has also been demonstrated.< >