In the realm of pragmatics, it is suggested that for a conversation to take place successfully, the speakers involved should be cooperative. The criterion of success in a conversation is much more significant in case of settling oral disputes. Online encyclopaedia of law defines dispute as “an assertion of a right, claim or demand on one side met by contrary claims or allegations on the other”. Thus, settling this controversy or disagreement, entails a more cooperative role for the speakers. Drawing on the framework of conversation analysis, the present study focuses on the use of Grice's cooperative maxims in oral arguments with the intention of finding out what cooperative maxims are more frequently abided and what maxims are more frequently violated by Persian speakers engaged in oral disputes in Iranian Dispute Settlement Council. For this purpose, three council meetings in Isfahan branch were recorded, transcribed, and analyzed. It was found that “quantity” and “relevance” were the two maxims more frequently violated during the disputes. Additionally, maxim of “quality” and “manner” were the ones most followed. Finally, the implications of the findings are discussed.