In this paper we present an Appraisal Theory grounded Lexicon for Evaluative Language (EvalLex) for both the English and the Greek language that is designed to enable a given Sentiment Analysis (SA) system to accurately detect two specific SA insights; “criticism” for negative evaluations and “praise” for positive evaluations. Each EvalLex entry is assigned a particular label based on a novel three-way classification schema. The experimental evaluation confirms the validity of the classification and provides promising results about the effectiveness of the introduced categories, as well as about the representativeness of the examined insights across different domains and media for both languages.