Formal Concept Analysis, as a mathematical tool, has been applied successively in diverse fields such as data mining, conceptual modeling, social networks, software engineering, and the semantic web, to cite but a few. One of the utter shortcoming of Formal Concept Analysis, however, is the large number of formal concepts that are extracted from even reasonably sized formal contexts. This overwhelming number was a key hindrance for a larger utilization of the technique (FCA). To overcome this shortcoming, only extracting a minimal coverage of formal concepts could be a remedy. Even though this task has been shown to be NP-hard, it attracted the attention of many researchers. In this paper, we introduce a new gain function based approach, called QualityCover, for the extraction of a pertinent coverage of a formal context. This algorithm operates akin to a greedy approach and relies on the assessment of a measure of correlation for the selection of the formal concepts to be retained in the final coverage. Extensive experiments show that QualityCover obtains very encouraging results versus those obtained by pioneering approaches in the literature.