Frankfurt-style cases (FSCs) are supposed to constitute counter-examples to the principle of alternate possibilities, for they are cases in which we have the intuition that an agent is morally responsible for his action, even though he could not have done otherwise. In a recent paper, Swenson (2015) rejects this conclusion, on the basis of a comparison between standard FSCs, which typically feature actions, and similar cases involving omissions. Because the absence of alternate possibilities seems to preclude moral responsibility in the cases of omissions, and because there is no morally relevant difference between the cases of actions and omissions, Swenson concludes that agents are not morally responsible in standard FSCs. In the present paper, I argue that Swenson's argument fails because there are at least two very important differences between both types of cases. First, there is a difference about whether agents in such cases actually perform the relevant action: while agents actually perform the relevant action in standard FSCs, they do not in FSCs supposedly involving omissions, for omissions require the possibility to have done otherwise. Second, while the agent's behavior in standard FSCs actually explain that he performed the relevant action, the agent's behavior in FSCs including omission actually fails to explain why the agent did not perform the relevant action. Beyond Swenson's argument, I end up discussing what factors ultimately explain (and justify) our intuitions about FSCs involving omissions.