In this paper, we motivate, propose and defend the following two conditions as individually sufficient and disjunctively necessary for moral responsibility: PODMA —originally proposed by Coren, Acta Analytica, 33, 145–159,, now cast as sufficient rather than necessary—and the TWC*, which amends versions presented by Young, 961–969, 2016; Philosophia, 45, 1365–1380, 2017). We explain why there is a need for new necessary and sufficient conditions, how these build on and improve existing ideas, particularly in relation to Frankfurt-style counterexamples and the continuing (...) discussion on their effectiveness, and why PODMA and the TWC* are good candidates. Finally, we defend the proposal against anticipated objections in order to clarify why we think these individually sufficient and disjunctively necessary conditions are plausible and able to inform the ongoing debate on the role of alternate possibilities in the ascription of moral responsibility. (shrink)