"Radical" libertarians believe that one's actions are not determined by anything prior to a decision, including one's character and values, and one's feelings and desires, in short, one's motives and reasons. Their model of free will is not "reasons responsive."

This idea, that determination by reasons and motives implies or entails strict causal determinism or even pre-determinism, is the Determination Fallacy.

Radical libertarians insist that pure chance, irreducible randomness, or quantum indeterminacy, must be involved directly in our decisions as causes of our thoughts and actions.

By contrast, "Modest" - or "Adequate" or "Conservative" - libertarians believe that humans are free from strict physical determinism - or pre-determinism, and all the other diverse forms of determinism. But they do not believe that chance is the direct cause of actions. That would preclude control of the agent's actions and deny moral responsibility.

Two-stage models of free will also require determination of the action by the agent's motives and reasons, following deliberation and evaluation of the alternative possibilities for action provided by that indeterminism.

Critics of libertarianism (determinists and compatibilists) are really attacking the radical libertarian view. If an agent's decisions are not connected in any way with character and other personal properties, they rightly claim that the agent can hardly be held responsible for them.

Many determinists and compatibilists now accept the idea that there is real indeterminism in the universe. Conservative libertarians agree with them that if indeterministic chance were the direct direct cause of our actions, that would not be freedom with responsibility.

Even determinists might also agree that if chance is not a direct cause of our actions, it would do no harm to responsibility. In which case, conservative libertarians should be able to convince determinists that if chance is limited to providing real alternative possibilities to be considered by the adequately determined will, it provides an intelligible freedom and can explains creativity.

Conservative libertarians can give the determinists, at least the compatibilists, the kind of freedom they say they want, one that provides an adequately determined will and actions for which we can take responsibility.

Even the current chief spokesman for libertarianism, Robert Kane admits that "radical" libertarian accounts of free will are unintelligible. No coherent idea can be provided for the role of indeterminism and chance, he says.

But Kane insists that "something more" is needed beyond simple determination of our thoughts and actions by our desires and feelings, our character and values, and our motives and reasons.

Yet, as Dennett and Mele also admit, a causal indeterminist view of this deliberative kind does not give us everything libertarians have wanted from free will. For Mike does not have complete control over what chance images and other thoughts enter his mind or influence his deliberation. They simply come as they please. Mike does have some control after the chance considerations have occurred.

The evaluation of alternative possibilities is of course only adequately determined

But then there is no more chance involved. What happens from then on, how he reacts, is determined by desires and beliefs he already has. So it appears that he does not have control in the libertarian sense of what happens after the chance considerations occur as well. Libertarians require more than this for full responsibility and free will. What they would need for free will is for the agent to be able to control which of the chance events occur rather than merely reacting to them in a determined way once they have occurred.

Yet, as Mele points out, while this causal indeterminist view does not give us all the control and responsibility that libertarians have wanted, it does give us many of the things they crave about free will (an open future, a break in the causal order, etc.). And it is clearly a possible view. Perhaps it could be further developed to give us more; or perhaps this is as much as libertarians can hope for.
(A Contemporary Introduction to Free Will, p.64-5)

Two-stage models for free will, especially the latest I-Phi Cogito model that has located the contribution of randomness as noise in information processing, leads us to a new conservative libertarianism that is less "free" perhaps than radical libertarianism, but distinctly more "willful" and more responsible.