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It has been recognized for some time that reflections back into the cavity of an injection laser from a mechanically unstable external mirror cause noise in the output of the laser (reflection noise). In this paper, noise measurements are presented for index-guided lasers as functions of the output power, the degree of optical isolation and external cavity length (5-15 cm), while current modulation (using 2-4 mA at 50-200 MHz) has been used to reduce the noise levels by as much as 20 dB. It is demonstrated that the mechanism of noise reduction by modulation is the frequency modulation of the laser's spectrum and its interaction with the modes of the external cavity. It is shown that using an optical isolator can give a relative intensity noise of -110 dB while using modulation in addition can reduce this to -125 dB; the bandwidth performance of optical storage systems is discussed in terms of these two schemes.