The minimum description length principle in wavelet denoising can be extended from the standard linear-quadratic setting in several ways. We describe briefly three extensions: soft thresholding, histogram modeling and a multicomponent approach. The MDL hard thresholding approach based on the normalized maximum likelihood universal modeling can be extended to include soft thresholding shrinkage, which can be considered to give better results in some applications. In MDL histogram denoising approach the assumptions of the parametric density models for the data can be relaxed. The informative and noise components of the data are modeled with equal bin width histograms. The method can cope with different noise distributions. In multicomponent approach more than one non-noise components are included in the model, because it is possible that in addition to the random noise there may be other disturbing signal elements, or that the informative signal is comprised of several different components which we may want to observe, separate or remove. In these cases adding informative components in the model may result result in better performance than in the NML denoising approach.