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This paper deals with the problem of wrapper feature subset selection (FSS) in classification-oriented datasets with a (very) large number of attributes. In high-dimensional datasets with thousands of variables, wrapper FSS becomes a laborious computational process because of the amount of CPU time it requires. In this paper we study how under certain circumstances the wrapper FSS process can be speeded up by embedding the classifier into the wrapper algorithm, instead of dealing with it as a black-box. Our proposal is based on the combination of the NB classifier (which is known to be largely beneficial for FSS) with incremental wrapper FSS algorithms. The merit of this approach is analyzed both theoretically and experimentally, and the results show an impressive speed-up for the embedded FSS process.