The paper is based on the following two assumptions. Firstly, evasive utterances are those which are semantically irrelevant to the question they are an answer to. Secondly, they can be divided into two main categories — overt and covert. The question to be asked as regards covert evasion is: How is it possible that an evasive speaker can nevertheless count on her/his utterance being considered cooperative? The objective of this paper is to analyse the means which are used by evasive speakers to pretend that their utterance does cooperatively answer the question and thereby meet its conversational demand. Semantic and pragmatic means were identified as serving the purpose of concealing evasive action. Within the former ones operation within the same topic as the questioner, and, secondly, equipping her/his evasive utterance with some formal characteristics which may indicate its relationship with the question, were listed. On a pragmatic level, the speaker may explicitly or implicitly indicate her/his willingness to answer the question: by statement or implication as well as licenses of uncooperativeness or hedging.