I explore some of the interconnections between inferences that participants make about one another’s (verbal) conduct, the implications they attribute to prior turns at talk, and the indirectness with which recipients may respond to enquiries – in short, the interconnections between inference, implication and indirectness. These are explored in the context of naturally occurring conversations (UK and US), from the methodological perspective of Conversation Analysis. Because inference has come to be associated closely with Grice’s concept of implicature, I begin by setting out my reasons for not following Grice’s path, preferring instead to revert to ‘implication’, namely the implication that a recipient finds in and attributes to a prior turn. My purpose here is to avoid the cognitive conceptualisation of speakers’ intentions that Grice supposed are associated with implicature. I argue that inference features in the understanding of and response to all turns at talk; it is not restricted to some special kind of utterance, as seems to be conveyed in Grice’s conceptualisation. The inferences that recipients make are evident in cases in which they respond not to what the prior speaker asked ‘literally,’ but to the inferred agenda of an enquiry. Moreover, recipients may respond indirectly to prior enquiries, thereby ‘side-stepping’ implications they attribute to those enquiries. In various ways, inference and indirection may on occasions be associated with practices for avoidance in conversation.