A new approach to blind source separation (BSS) in the wavelet domain is introduced. The technique improves the speed of convergence of the natural gradient algorithm (NGA), and overcomes the problem of having to select the non-linearities required to separate mixed sub- and super-Gaussian signals. The distribution of the wavelet coefficients of certain natural source signals is modeled by a Laplacian density, and therefore in the time-scale domain the problem of selecting an appropriate activation function is overcome. Experimental results show the validity of this method.