The idea of using responsibility in the allocation of healthcare resources has been criticized for, among other things, too readily abandoning people who are responsible for being very badly off. One response to this problem is that while responsibility can play a role in resource allocation, it cannot do so if it will leave those who are responsible below a “sufficiency” threshold. This paper considers first whether a view can be both distinctively sufficientarian and allow responsibility to play a role even for those who will be left with very poor health. It then draws several further distinctions that may affect the application of responsibility at this level. We conclude that a more plausible version of the sufficientarian view is to allow a role for responsibility where failure to do so will leave someone else who is not responsible below the sufficiency threshold. However, we suggest that individuals must exhibit “sufficient responsibility” in order for this to apply, involving both a sufficient level of control and an avoidable failure to respond adequately to reasons for action.