Soft thresholding has been a standard wavelet de-noising procedure in many signal and image processing applications. Theoretically, it is also almost optimal in the sense of nearly achieving the minimax mean-squared error. Inspired by this property, this paper proposes the addition of coefficient de-noising before soft thresholding. This extra step serves to reduce noise in the empirical wavelet coefficients at each scale, and can be shown to yield a lower mean-squared error. Moreover, we advocate the use of the translation-invariant dyadic wavelet transform, together with an approximate self-dual wavelet, instead of the discrete wavelet transform (DWT) in performing de-noising. Experiments show that the proposed method improves the signal-to-noise ratios of the de-noised signals. Moreover, the de-noised signals do not have artifacts typically associated with DWT-based methods.