An interferometric fiber optic gyro (IFOG) measures rotation by comparing the propagation time of optical signals transmitted in opposite directions around a coil of optical fiber. An important constraint on accuracy is the thermally induced nonreciprocity which can occur when there is a localized time-dependent thermal expansion in a section of the fiber. In order to prevent measurement error due to thermally induced nonreciprocity, the commonly used IFOG coil geometry, called quadrupole winding, features layers after the innermost wound in pairs, each layer pair beginning with a fiber element on the opposite side of the innermost layer from that of the preceding layer pair. This alternating layer pair arrangement is needed so that any thermal gradient present in the coil structure will be symmetrical about the center of the fiber loop, with the important desirable result that time of flight variations for the two opposite transmission directions due to time varying thermal expansion cancel one another. Although the principle is sound, such windings are difficult to realize in practice because the alternating layer pair geometry tends to allow winding flaws which degrade precision and make reliable production of the winding difficult. OPTELECOM has devised methods for making flawless level quadrupole windings between flanges which facilitate maintaining the precision required for IFOG coils. Under DARPA/U.S. Army Contract DAAH01-90-C-0520, the authors investigated application of these methods to low manufacturing cost IFOG coil winding implementation. A summary of IFOG coil winding constraints, discussion of winding techniques which lead to low-cost winding while satisfying constraints, and results of initial cost reduction work are presented.