||MNDL denoising is an adaptive, data-driven thresholding method based on a recently developed idea of Minimum Noiseless Description Length (MNDL). MNDL Subspace Selection (MNDL-SS) is a novel method of selecting an optimal subspace among the competing subspaces of the transformed noisy data. I extended the application of MNDL-SS for thresholding purposes. The approach searches for the optimum threshold for the data coefficients in an orthonormal basis. It is shown that the optimum threshold can be extracted from the noisy coefficients themselves. While the additive noise in the available data is assumed to be independent, the main challenge in MNDL thresholding is caused by the dependence of the additive noise in the sorted coefficients. The approach provides new hard and soft thresholds. Simulation results are presented for orthonormal wavelet transform. MNDL denoising is comparable with the existing thresholding methods and in some cases outperforms them.