Lean is widely applied in hospitals, but the impact tends to be limited. This paper investigates three possible explanations: 1) maturity, 2) complexity, and 3) the value concept and analyses the bearing of these in a case study of lean application in a large Danish university hospital. The results indicate that lean tends to be applied in secondary and support functions with a logistic character and therefore has had a limited impact on the overall healthcare performance. The case study shows that there are constraints related to low lean maturity, the complexity of processes and operations as well as differences in value perceptions among the different professions (e.g., doctors, nurses, and managers) within the hospital. The conclusion is that lean is useful for hospitals, but the lean concept as well as its implementation methods need to be fitted to the organizational complexity and diverging values in hospitals in order to bring about a larger impact. It is therefore necessary to develop new models for the lean concept as well as the implementation of lean adapted to the particular context of hospitals with a stronger focus on patient experiences and on coordination of social relations.