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This paper reports on a new mechanism to decrease the number of averages and, consequently, the measurement time of Brillouin optical time-domain analysis (BOTDA) sensors using wavelet shrinkage techniques. Two different wavelet shrinkage techniques, VisuShrink and SureShrink, are applied to denoise signals acquired from measurements in BOTDA sensors. The conventional method to denoise signals in BOTDA sensors is ensemble averaging. Ensemble averaging is a time consuming technique, as it requires many acquisitions of signals to provide an acceptable SNR. To reduce the number of acquisitions, the setup of the BOTDA sensor is modified to denoise acquired signals using VisuShrink or SureShrink before applying ensemble averaging. Experimental results show a significant reduction in the number of averages required to provide an accurate measurement, and consequently, a substantial saving in the measurement time of the sensor. It has been shown that the combination of ensemble averaging with VisuShrink or SureShrink reduces the measurement time of the sensor up to 90%. This reduction in the measurement time enables the implementation of dynamic and fast measurements with BODTA sensors and opens opportunities to target a new range of applications.