This work improves on the FTNB algorithm to make it more tolerant to noise. The FTNB algorithm augments the Naïve Bayesian (NB) learning algorithm with a fine-tuning stage in an attempt to find better estimations of the probability terms involved. The fine-tuning stage has proved to be effective in improving the classification accuracy of the NB; however, it makes the NB algorithm more sensitive to noise in a training set. This work presents several modifications of the fine tuning stage to make it more tolerant to noise. Our empirical results using 47 data sets indicate that the proposed methods greatly enhance the algorithm tolerance to noise. Furthermore, one of the proposed methods improved the performance of the fine tuning method on many noise-free data sets.