The past decade has seen an increased focus on body movement in computer games. We take a step further to look at body games: games in which the main source of enjoyment comes from bodily engagement. We argue that for these games, the physical and social settings become just as important design resources as the technology. Although all body games benefit from an integrated design approach, the social and physical setting become particularly useful as design resources when the technology has limited sensing capabilities. We develop our understanding of body games through a literature study and a concrete design experiment with designing multiplayer games for the BodyBug, a mobile device with limited sensing capabilities. Although the device was designed for free and natural movements, previous games fell short in realizing this design ideal. By designing the technology function together with its physical and social context, we were able to overcome some of the device limitations. One of the games was subsequently incorporated in its commercial release.