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It is widely accepted that spinning a fiber while it is drawn is one of the most effective way to reduce its polarization mode dispersion. In this paper, the mean square differential group delay of rapidly, periodically spun fibers is analyzed by means of a theoretical model with a wide range of validity. It is shown that under particular conditions, and in contrast with the common sense, the spinning process may actually increase the fiber differential group delay rather than reducing it. This effect depends on the autocorrelation function of the intrinsic birefringence of the fiber and may be achieved by properly tuning the spin function.