This paper explores the relevance of a specific kind of sensed connectedness or 'teleo-affectivity' to the organisation and enactment of end-of-life care. Referred to as heedful inter-relating, this teleo-affective connectedness has been found to occur among employees as they carry out their highly complex and dangerous work. This paper focuses on the proposals put in the literature for confronting the complexity of end-of-life care in the intensive care unit (ICU), and inquires into the positionings incurred in and around end-of-life care in one specific unit, with the aim of gauging the pertinence of heedful inter-relating to end-of-life care in ICU. The paper argues that while several commentators appear to be calling for enhanced heedful conduct in end-of-life care, ICU practices may not admit the kind of heedful inter-relating that is evident in high-reliability organisations such as nuclear aircraft carriers. We suggest it may be unwise to gauge intensive care units' complexity purely against the brief of realising cultural scripts of the dying, and that ICU in fact manifests a broader societal concern necessitating a more variegated composition: to devise multiple ways to contain the impression and impact of (the meaning) death for society (societies) generally.