A wavelet-transform (WT)-based power-quality (PQ) monitoring system captures voltage and current waveforms, when magnitudes of WT coefficients exceed the set threshold values across the scales. A lot of literatures has proposed several methods based on WT to detect and classify PQ disturbances. But a problem in the practical implementation of the wavelet-based triggering method is the presence of noise, riding on the signal. The presence of noise not only degrades the detection capability of wavelet-based PQ monitoring systems but also hinders the recovery of important information from the captured waveform for time localization and classification of the disturbances. Therefore, to enhance the performance of WT-based monitoring systems and to improve the classification accuracy of WT-based classifiers, two standard statistical hypothesis test-based denoising procedures have been proposed in this paper. Extensive tests conducted on the data obtained from simulations of a practical distribution system confirm the effectiveness of the proposed approaches in denoising of the PQ waveforms.