This study compares between two common approaches to discourse analysis: Gricean pragmatics theory and politeness theory. Data have been collected from a daily conversation between two speakers. The data have been analysed by using the framework of Gricean theory, which was established by Grice (1975), and also politeness theory, which was proposed by Brown and Levinson (1978) along with Leech (1983). The results show that politeness theory is more suitable than Grice’s theory for analysing daily conversation; this is because both Brown and Levinson’s (1978) and Leech’s (1983) frameworks can explain the reasons why speakers use indirect ways to convey certain messages to the hearer, for example to avoid Face-Threatening Acts (FTA). In addition, indirect conveyance makes the listener feel comfortable, but Grice’s model does not explain the reasons for this indirectness