Using Conversation Analysis, the author analyzes naturally occurring audiotaped conversations from colloquial Algerian Arabic, focusing on the act of complimenting. The analysis includes complimenting relative to topic progressivity, complimenting in compliment-trigger situations, complimenting as a response to self-deprecation, and the co-occurrence of compliments and divine invocations. These topics , the author claims, have been underexplored (or even unexplored) in compliments and compliment responses literature, including on-command compliments, discursive creativity, complimenting as a multi-turn speech event, recycled compliments, and the employment of self-deprecation and the compliment it triggers as interactional resources. The merits of this paper lie in its focus on a comparatively understudied variety or Arabic and in its use of natural conversations - unlike so many existing studies on Arabic compliments and compliment responses.