In many parts of the developed world, families engage with a wide range of communication media as a part of their daily lives. Parents often express mixed feelings about this engagement on the part of young people, however. Employing Baumberg's narrative-in-interaction analysis to interviews with 55 parents and 125 young people, this article explores both the discursive strategies parents employ when discussing their rules and regulations regarding digital technologies, and the strategies employed by their teenage young people in response. It considers how parents attempt to articulate authority in relation to digital media use among their teenage children, and how the ways in which teens interpret those parental attempts to express authority influence the strategies they themselves embrace regarding digital media. The article argues that although economically disadvantaged families experience the digital generation gap with particular intensity, their strategies reveal that they and their teenage children are able to deal with these challenges in creative and effective ways.