The Naïve Bayes has proven to be a tractable and efficient method for classification in multivariate analysis. However, features are usually correlated, a fact that violates the Naïve Bayes' assumption of conditional independence, and may deteriorate the method's performance. Moreover, datasets are often characterized by a large number of features, which may complicate the interpretation of the results as well as slow down the method's execution. In this paper we propose a sparse version of the Naïve Bayes classifier that is characterized by three properties. First, the sparsity is achieved taking into account the correlation structure of the covariates. Second, different performance measures can be used to guide the selection of features. Third, performance constraints on groups of higher interest can be included. Our proposal leads to a smart search, which yields competitive running times, whereas the flexibility in terms of performance measure for classification is integrated. Our findings show that, when compared against well-referenced feature selection approaches, the proposed sparse Naïve Bayes obtains competitive results regarding accuracy, sparsity and running times for balanced datasets. In the case of datasets with unbalanced (or with different importance) classes, a better compromise between classification rates for the different classes is achieved.