Since the 1970s, an international market has been growing in the production and sale of fabric specifically woven for ‘babywearing’. These ‘wraps’, a simple piece of cloth for baby carrying, have a long tradition throughout the world but are increasingly marketed to ‘high-end’ collectors as well as ‘modern’ young parents. New releases of limited edition and boutique ranges create competition over highly desirable and often quite unattainable wraps that must be tempted out or awaited in the second-hand forums. The community describes the search for these desperately desired goods as the search for ‘unicorns’. But obtaining one’s unicorn requires others to part with material objects made incommensurable through the intimate, inter-embodied ‘skinship’ practice of wrapping and carrying a child. This article explores how the emotional entanglement of these second-hand goods is negotiated through an emerging exchange etiquette that attempts to protect the illusion that one is trading in incommensurable goods.