This paper tackles problems where attribute selection is not only able to choose a few features but also to achieve a low performance classification in terms of accuracy compared to the full attribute set. Correlation-based feature selection (CFS) has been set as the baseline attribute subset selector due to its popularity and high performance. Around hundred data sets have been collected and submitted to CFS; then the problems fulfilling simultaneously the conditions: (a) a number of selected attributes lower than six and (b) a percentage of selected attributes lower than a forty per cent, have been tested onto two directions. Firstly, in the scope of data selection at the feature level, an advanced contemporary approach have been conducted as well as some options proposed in a prior work. Secondly, the pre-processed and initial problems have been tested with some sturdy classifiers. Moreover, this work introduces a new taxonomy of feature selection according to the solution type and the followed way to compute it. The test bed comprises seven problems featured by a low dimensionality after the CFS application, three out of them report a single selected attribute, another one with two extracted features and the three remaining data sets with four or five retained attributes; additionally, the initial feature set is between six and twenty-nine and the complexity of the problems, in terms of classes, fluctuates between two and twenty-one, throwing averages of sixteen and around five for both aforementioned properties. The contribution concluded that the advanced procedure (extended CFS) is suitable for problems where only one or two attributes are selected by CFS; for data sets with more than two selected features the baseline method is preferable to the advanced one, although the considered feature ranking method achieved intermediate results.