This study is primarily concerned with the issue of determining whether it is worthwhile to try to teach the correct pronunciation of subphonemic segments in ESL courses, focusing specifically on Flapping in North American English (NAE). It begins by examining how inadequately phonology textbooks have generally treated Flapping and goes on to provide a comprehensive description of this phonological process. Then, through an exhaustive examination of the ESL and TESL pronunciation manuals that have been published in the last 40 years or so, an assessment is first made of the manner and extent to which Flapping has been dealt with by the authors of such books. These findings are then compared with the opinions expressed by researchers in the field of second language education in order to determine what sort of consensus currently exists on this issue. The general conclusion is that since flaps are demonstrably the most salient of all NAE allophones and occur as phonemes in the first language of many ESL learners, these segments should be given due consideration in any pronunciation curriculum.