The noise induced by environmental perturbations, such as vibration in fibre leads, degrades the performance of an optical current-measurement system, and should be suppressed. Vibration-induced noise in three types of fibre leads, single-mode, highly birefringent, and multimode fibre, has been measured when used in such an optical current-measurement system, and the effect quantified and discussed. The results have shown that vibration-induced noise may be suppressed in highly birefringent fibre by choosing carefully the input angle of a linearly polarized beam or by using a low-coherence source in the sensor. The noise observed can be effectively eliminated by employing a long length of multimode fibre and a low-coherence source, combined with appropriate coupling conditions.