This article explores the nature of relationships formed between nuns and male clergy in early modern Venice. It is based on the records of trials for the violation of conventual enclosure, the principle at the centre of the reforms of nunneries decreed by the Council of Trent, which aspired to sever all links between nuns and the world outside the cloister. The trials offer detailed insights into the interactions of male and female celibates, whose relationships were frequently monogamous, long-term, and intense, although rarely overtly sexual. I argue that the constraints of enclosure conditioned the nature of celibate desire, promoting a model of heterosocial engagement in which bodily intimacy was surprisingly unimportant.