This paper presents a sociological investigation of instances of a class of claimed paranormal phenomena: the apparent demonstration of paranormal means of cognition by psychic practitioners, such as mediums, psychics, clairvoyants and tarot-card readers. Using a conversation analytic perspective, this paper examines recordings and transcripts of sittings between psychics and members of the public. It describes a linguistic sequence through which (unattributed) information is offered by the psychic, accepted by the sitter and then established as coming from a paranormal source. This form of analysis is located within an emerging social scientific interest to explore ostensibly anomalous human experiences to enrich understanding of everyday behaviour. In this case, it is argued that analysis of the socially organised properties of exchanges in which apparently successful demonstrations of paranormal cognitive abilities are accomplished can contribute to broader debates about the relationship between discourse and cognition.