To obtain high spatial resolution over a long sensing distance in Brillouin optical correlation domain reflectometry (BOCDR), a broad laser spectrum and high pump power are used to improve the signal-to-noise ratio (SNR). In this Letter, we use a noise-modulated laser to study the variation of the Brillouin spectrum bandwidth and its impact on the coherent length of BOCDR quantitatively. The result shows that the best spatial resolution (lowest coherent length) is achieved by the lowest pump power with the highest noise-modulation spectrum. Temperature-induced changes in the Brillouin frequency shift along a 253.1 m fiber are demonstrated with a 19 cm spatial resolution.