Propagation of solitons in fibers with randomly varying birefringence is studied with and without including the effect of soliton transmission control. A simple expression for the decay of soliton energy due to the birefringence is derived, which will be useful in predicting soliton-pulse broadening in randomly birefringent fibers with their polarization-mode dispersion parameter specified. It is also shown that transmission control of solitons effectively removes dispersive radiations generated by the birefringence.