The quest for something to give to Syria

This article in the Jerusalem Post offers several views on what Syria might demand from the U.S. in exchange for “cooperating” in the stabilization Iraq. Whichever view one embraces, the conclusion must be the same –the price is too high and the pay-off too low.
The obvious thing one would expect the Syrians to want in exchange for their cooperation is the return of the Golan Heights. Moreover, the Syrians have said this is what they want. According to the JPost, Ayman Abdel Nour, an official of the ruling Syrian Ba’ath party, has said that his country’s “top demand” is that the U.S. use its influence with Israel to secure the return of that territory. And one can understand why. Not only would the return of the Golan Heights improve Syria’s military situation in relation to its main enemy, it would also provide a huge boost in status for the Assad regime.
However, the JPost reporter is too sophisticated to take Syria at its word, so he embraces speculation that the Syrian’s fundamental demand will be to have the international tribunal investigating the assassination of former Lebanese prime Minister Rafiq Hariri called off, and to receive some sort of green light to increase their influence and involvement in Lebanon. In this account, the Syrians are “terrifed” of the tribunal because, supposedly, a judgment against Assad or those close to him would threaten the very survival of the regime.
It’s not clear to me why this might be the case. If it is, however, we should by no means agree to call off the dogs. Nor should we agree to countenance increased Syrian involvement in Lebanon. Why weaken the prospects for an improved future in both Lebanon and Syria in exchange for Syrian promises of good behavior in Iraq?
Indeed, one must ask what Syria could do to help in Iraq even if it were inclined to. The primary problem in Iraq right now is sectarian violence between Sunni and Shia factions. One can at least argue that Iran has some ability to reduce that violence. But I haven’t seen anyone try to make the case that Syria has that ability. In theory, Syria might be able to prevent some foreign fighters from entering Iraq. But at this point that would do little or nothing to reduce sectarian violence between Iraqis themselves.
Instead of making major concessions of whatever nature to Syria in exchange for general promises to police a porous border, why not concede that we won’t bomb Syrian military assets if the government makes measurable progress towards that goal?