In both popular and academic discussions of the use of algorithms in clinical practice, narratives often draw on the decisive potentialities of algorithms and come with the belief that algorithms will substantially transform healthcare. We suggest that this approach is associated with a logic of disruption. However, we argue that in clinical practice alongside this logic, another and less recognised logic exists, namely that of continuation: here the use of algorithms constitutes part of an established practice. Applying these logics as our analytical framing, we set out to explore how algorithms for clinical decision-making are enacted by political stakeholders, healthcare professionals, and patients, and in doing so, study how the legitimacy of delegating to an algorithm is negotiated and obtained. Empirically we draw on ethnographic fieldwork carried out in relation to attempts in Denmark to develop and implement Patient Reported Outcomes (PRO) tools - involving algorithmic sorting - in clinical practice. We follow the work within two disease areas: heart rehabilitation and breast cancer follow-up care. We show how at the political level, algorithms constitute tools for disrupting inefficient work and unsystematic patient involvement, whereas closer to the clinical practice, algorithms constitute a continuation of standardised and evidence-based diagnostic procedures and a continuation of the physicians' expertise and authority. We argue that the co-existence of the two logics have implications as both provide a push towards the use of algorithms and how a logic of continuation may divert attention away from new issues introduced with automated digital decision-support systems.