Abstract: We present our most recent results about an ongoing study addressing the comparison of various speckle reduction filters. In a previous work, we have concentrated on the best Signal-to-Mean-Square-Error (S/MSE) ratio provided by a complex Wavelet Coefficient Shrinkage (WCS) filter and several standard speckle filters. Here we specifically address the numerical behavior of the WCS filter over a change (1) in the regularity and type of the wavelet (orthogonal versus bi-orthogonal) and (2) in the wavelet coefficient thresholding type (soft- versus hard-thresholding). We also present measures of the variation of the S/MSE over a wide range of the WCS filter parameters in order to provide information on the optimal application range of the filter in practical situations. As in our previous work, tests are performed on optical imagery with a simulated multiplicative Log-Normal noise. The S/MSE ratio is measured after averaging the filtered images over 16 diagonal shifts of the Discrete Wavelet Transform (DWT) in order to approximate a shift invariant DWT. Our experiments show, among other, that the optimal threshold level depends on the spectral content of the image and that the soft-thresholding scheme is the best choice for images with high spectral content.