In this paper, we present the improved stimulated Brillouin-induced self-heterodyne (ISISH) method that overcomes the effect of amplified spontaneous emission (ASE) noise of erbium doped fiber amplifier (EDFA) on linewidth measurements. In addition, we eliminate the beating effects of additional sideband during the measurement of narrow laser linewidth. Moreover, we experimentally demonstrate the effect of amplified spontaneous Brillouin scattering (ASBS) noise on the variation of the measured linewidth of the laser under test (LUT) with varying pump power. We measure the Brillouin amplifier gain, which is essential for the ISISH technique, as 13.5, 12.7 and 9.5 dB at the pump powers of 16, 12 and 8 mW, respectively. These results are consistent with the analytical values of 14, 13 and 12.5 dB at the same variations in pump powers as previously reported. Experimental results show the 20 dB linewidths of 4, 6.7 and 10 kHz at pump powers of 16, 12 and 8 mW, respectively. We also perform the stimulated Brillouin-induced self-heterodyne (SISH) method. However, in SISH, the obtained linewidth of the LUT differs by approximately 4, 4.3 and 5 kHz at the pump powers of 16, 12, and 8 mW, respectively. Furthermore, we investigate the effect of detuning on LUT linewidth measurement in the ISISH method. The 20 dB linewidths at 5 and 10 MHz detuned from the Brillouin peak at 16 mW pump power are 20 and 25 kHz, respectively. These values are significantly larger than the measured linewidth at the pump power of 16 mW without detuning.