Working as clinical ethicists in an academic hospital, we find that practitioners tend to take a principle‐based approach to moral dilemmas when it comes to (not) treating patients who feel like a burden, in which respect for autonomy tends to trump other principles. We argue that this approach insufficiently deals with the moral doubts of professionals with regard to feeling that you are a burden as a motive to decline or withdraw from treatment. Neither does it take into adequately account the specific needs of the patient that might underlie their feeling of being a burden to others. We propose a care ethics approach as an alternative. It focuses on being attentive and responsive to the caring needs of those involved in the care process—which can be much more specific than either receiving or withdrawing from treatment. This approach considers these needs in the context of the patient's identity, biography and relationships, and regards autonomy as relational rather than as individual. We illustrate the difference between these two approaches by means of the case of Mrs K. Furthermore, we show that a care ethics approach is in line with interventions that are found to alleviate feeling a burden and maintain that facilitating moral case deliberation among practitioners can supports them in taking a care ethics approach to moral dilemmas in (not) treating patients who feel like a burden.