We utilize a recent form of the Nested Cavities (abbr. NC) classifier [1] from which a powerful new classification approach emerged. In this application there are many outliers in the datasets which we decided to judiciously remove. Further, working on the classification of Stage 3 we found wide dispersal in the data. After considerable experimentation we came to the conclusions that, at least between Stage2 and Stage3 some of the data has have been misclassified. By including some of the Stage2 data with values very close to those of Stage3 data and forming a New-Stage 3 ALL nine of the measured variables have tight value ranges and the whole data set visually appears as a well-defined cluster. In turn, accurate classification rules are obtained which had not been possible for the original partition into stages. These findings are explained, motivated and analyzed in this paper. Our thesis then is that some of the data has been misclassified in the original stage partition. This data is identified and new Stage 3 sets are formed whose classification reveals narrow range values of the measured waves providing a much clearer understanding of the sleep mechanism dynamics.