I've been thinking about some ways to fix Hobbes's view so that you don't end up giving up all your rights to a sovereign who then has absolute power and can do awful things with impunity. Hobbes was concerned that if you don't give up all your rights to a single individual or body, your divided government will be riven by internal power struggles and you'll end up in another English Civil War. (A lot of Leviathan is a "How to not be in the English Civil War" manual.) Hobbes claimed that an absolute monarch would rule in the best interest of his subjects because his power was constituted by theirs. Historically, this consideration hasn't been especially successful in aligning the interests of absolute monarchs with their subjects.
So here's a way to start from Hobbes' basic premises about the state of nature and meet all his major desiderata while incorporating goodies like separation of powers and the structures of liberal democracy. Rather than getting out of the state of nature by giving up all your rights to a sovereign, give them all up to a form of government embodied in a clearly written Constitution, which defines the roles of various branches of government, lays out procedures for governance, and guarantees a bunch of rights to the subjects. You're also going to have to do some voting to figure out who will fill the offices at first, but Hobbes grants that you can do that in his account of how a commonwealth begins by institution.
From then on, regard the Constitution the way that Hobbes would want you to regard the sole pronouncement of an absolute monarch. If people are violating it, they're denying the sovereign's authority, putting them at a state of war with everyone else. Assuming that the Constitution is clearly written and there's an agreed-upon framework for interpreting it, I don't see why you couldn't achieve all of Hobbes' major desiderata. (There are some minor things you couldn't get -- he thinks an absolute monarchy is superior to democracy because the absolute monarch has an easier time making secret plans. But I'm sympathetic to Yglesias' argument that in some foreign policy contexts, it actually helps if everyone knows you're incapable of secrecy.)
This isn't to say that there aren't problems with this account of government. The point is just that as far as I can tell, it'd accomplish everything Hobbes really cares about, while building in some extra goodies.