Moral responsibility and could-have-done-otherwise

Sometimes people say that moral responsibility requires free will, i.e., that we can act freely.

(T2)  For any person x who performs an action A,
x can be held morally responsible for A = iff
x performs A freely. 

But we can go further. We might assume that moral responsibility requires the sort of free will where we could have done otherwise. After all, when we say 'you should not have done what you did do', or 'you should have done what you did not do', we seem to be implying that you could have done otherwise. So if we assume that free will is this:

(T1*)  For any person x who performs an action A,
x performs A freely = iff
x could have done other than A,
given the same history.

Then one could say:

(T3)  For any person x who performs an action A,
x can be held morally responsible for A = iff
x could have done other than A,
given the same history.