The free will debate is usually characterized as a dispute about whether or not freedom is compatible with determinism. Determinism is understood as the doctrine that all events are subject to the laws of nature, which admit of no exceptions. So an act like raising your arm falls under natural laws, which guarantee that in the same antecedent conditions the same action will be performed. The question then is whether freedom is consistent with the uniformity of nature: does determinism in the defined sense rule out free will or is it compatible with free will (and perhaps conducive to it)? The first point I want to make is that this is not quite the right way to put the issue: the question isn’t about whether freedom is compatible with determinism in the sense defined—that is just one form of the question. The general question, of which this is a special case, can be put in a variety of ways and it useful to have a sense of these ways: Is freedom compatible with determination, causation, psychological and physical laws, constraint, necessity, dependence, fixation, supervenience, grounding, predictability, forcing, compelling, being subject to, being based on, being conditioned by, being controlled by, being in the grip of, being the result of? That is, if an action A is in accordance with a desire D, can A be free if it bears any of these relations to D? Put most generally, is freedom of action compatible with dependence of some kind? The compatibilist says yes while the incompatibilist says no. The strong compatibilist (as I define him) holds that freedom requires such dependence, as well as being consistent with it; but the further spelling out of the nature of the dependence is not yet stated. So far it is an abstract placeholder.
This leaves room for a formulation not equivalent to the traditional formulation in terms of determinism, namely whether freedom is compatible with causation without laws. Suppose my desire D causes my action A but there is no law subsuming that causal relation, so that D can occur without A and A without D. Then determinism does not apply to A, though there can be a debate about whether the causation involved rules out freedom (or rules it in). This is because there is still a type of dependence that (allegedly) calls into question the freedom of the action. The claim is that A had to happen given D, and this conflicts with freedom (assuming that freedom requires the ability to have done otherwise). Laws are not the essential consideration here; so denying laws will not save free action from some kinds of incompatibilism. The abstract issue is whether any kind of dependence rules out freedom, where this dependence might not even be causal dependence (as in occasionalism). The question is whether the action follows from the desire in some way (perhaps in conjunction with other psychological states), and laws need not be the only reason for this. Any kind of consequence will generate the problem.
The strong compatibilist should not then assert that free will implies determinism, as if there can only be free will in a world governed by exceptionless laws; what she should assert is that it is essential to freedom that actions depend on desires in some way, leaving it open what the metaphysics of this dependence might be (suppose she rejects causation and laws on metaphysical grounds). There might be some weird kind of dependence mediated by a capricious God whereby actions are connected to desires; what matters is that the action follows from the desire in some way instead of being quite independent of the desire. We might then say that the dispute concerns the consequences for freedom of desire-dependence, however that is to be understood. The uniformity of nature is a side issue.
The position I am inclined to accept is that freedom entails desire-dependence (strong compatibilism); and the question this position prompts is whether such dependence is compatible with accepting that agents have an ability to act otherwise than they actually act.  Much ink has cascaded around this question, but I propose to be brief and dogmatic here: “I could have done otherwise” means “I had a choice”. It does not mean any fancy metaphysical business about the course of nature, such as that my actions could flout the laws of nature. It does not mean that two worlds could be exactly alike in their laws of nature and initial conditions and yet agents act differently in those worlds, or that two people could be exactly alike psychologically and yet choose differently. It means simply that I was not constrained by some outside (or inside) force that prevented me from doing what I wanted all things considered. When the gun is to your head you have no choice, as we say, but when you act as you see fit you have a choice—and that is all it means to say that you could have acted otherwise. The phrase carries no metaphysical baggage about the world having alternate futures despite what has obtained so far. And you have a choice even if your actions depend on your desires in some way—indeed that is what choice is. So choice can exist in a world in which actions depend on desires. Choice is compatible with desire-dependence. Intuitively, the ability to act otherwise is a matter of making different choices in the light of different desires, beliefs, perceptions, hunches, personality traits, and so on. It doesn’t require some remarkable capacity to transcend the empirical world and just insert an action into history without any intelligible antecedents.
I see nothing wrong or misleading about expressing strong compatibilism as the thesis that freedom entails psychological determination (specifically by desires, but not only desires), where this need not imply determinism (though I also believe in determinism about our world). The type of determination in question need not fit any other type of determination in nature, and may indeed be quite mysterious; all that matters is that action not be decoupled from desire (and other psychological states) in the way libertarians sometimes envisage. We are not even required to call the dependence a type of causal relation, still less to assimilate it to other types of causal relation. All we need to say is that the agent acted as he did because of his desires (etc.)—and not because he was compelled so to act by someone with power over him (or anything similar). The essential point is that the strong compatibilist is not committed to holding that actions fall under laws, whether strict or merely statistical; all that is entailed by the concept of a free action is some sort of dependence or determination. This is what the concept of freedom requires, not that actions fall under laws or that they are subject to causality. Equally the incompatibilist does not have to establish the uniformity of nature and the universal reach of causality in order to mount his case against freedom—he just needs a general abstract notion of dependence. The issue between them has thus been improperly formulated and should be recast in the manner suggested here.
I shall end with a point that I have not seen made: that there is no merit in having a capacity for freedom that involves desire-independence. Suppose it is claimed that two individuals could be exactly alike psychologically (and possible also physically) and yet act differently. That would mean that their different actions correspond to no difference of desire. But what would be the point of being able to act in ways that are independent of desire—what would that get you? Not greater desire satisfaction certainly, nor greater rationality (all the beliefs are the same too). It seems like a gratuitous talent to flout your own psychology, as if you are trying to prove some supernatural gift—“Look, I can act in ways that don’t satisfy my desires or reflect my outlook on the world!” Why would such a capacity exist in us? Do other animals have it, including our closest relatives? What about children? How could it evolve? It seems like a bizarre kind of spontaneity, serving no purpose except to establish a dubious metaphysics. If this is what freedom is, what is the point of being free? No, freedom is the ability to act on your own desires and reasoning, making sure you get what you want when you want it. That is something we can all get behind. You want your choices to be shaped by your desires (including your moral desires) not to be miraculously uncoupled from your desires. It isn’t that things would be better for us—we would be a better class of being–if we were able to act in ways that contravene our carefully considered desires and judgments. That just seems like a pointless eccentricity, nothing to celebrate.
 See my papers “Freedom as Determination”, “I’m Free”, and “Freedom Within Necessity”. I defend this kind of compatibilism in these papers and say more what it means to say that someone could have done otherwise.