President Obama is in a huge jam on Syria, and it’s not clear how he gets out of it. The problem is twofold. First, he is preparing to take military action against Syria for the sole purpose of enforcing international law. Yet he has very little support from the organizations—or many members of those organizations—that are charged with enforcing international law. If the point of the intervention is to uphold the civilized world’s long-held norms (in this case, norms against the use of chemical weapons), and if he can’t persuade more than a couple other countries to go along, then he doesn’t have a very potent case.

This is not a technical-legal question. It’s central to the strategy and effectiveness of whatever sort of military action he might decide to launch. In his Aug. 28 PBS interview, Obama said that an attack, if he launched one, needed to send “a pretty strong signal that” Bashar al-Assad’s regime “had better not do it again”—i.e., had better not launch any more chemical weapons. And yet if Assad doesn’t see the world closing in on him, if he sees the attack as purely an American (or Western) campaign, against which he can mobilize the usual anti-American (or anti-Western) actors, then the “signal” is going to be pretty weak.

It must have come as a shock when the British Parliament voted down a motion to authorize military action, especially after Prime Minister David Cameron promised Obama that he would join an international coalition to punish Assad for his monstrous acts. Cameron may have thought the motion was a slam dunk. Not since 1782 has a British leader lost a war resolution (the last time was when Parliament decided, against the King’s urgings, to withdraw from the American Colonies). It’s unclear whether this defeat reflects Cameron’s weakness or Britain’s abdication of a role in global politics. But it’s clear in retrospect that Obama should have lined up his ducks before letting his top aides all but announce that the cruise missiles were on their way.

French President François Hollande, who doesn’t need his Parliament’s approval for such things, has said he will join Obama in the war (the first time the two countries have allied in battle without Britain since they jointly fought against Britain in the American Revolution). The Germans are reluctant. The Arab League is wavering, as usual. (Silent support is about all one can expect, though the Saudis have lately been shipping lots of weapons to the rebels in southern Syria). The Turks? Unclear, though their support is crucial, since Turkey is one of the few countries that could claim “self-defense,” as it sits on Syria’s northern border and would potentially face the fallout from a future chemical attack. And since it’s a member of NATO, Turkey could also invoke Article 5 of the North Atlantic Treaty (an attack on one member is an attack on all) to rally the other allies.

But the second problem Obama faces is at least as serious. He has to figure out how to launch an attack that accomplishes his objectives—and that means first figuring out what those objectives are. He outlined what they weren’t in his PBS interview.

For instance, he said, “I’ve … concluded that direct military engagement, involvement in the civil war in Syria, would not help the situation on the ground.” So, one can surmise (in fact, it has long been clear) that one of his objectives is not to help the rebels win the war or to help topple Assad’s regime.

On a related point, he said, “I have no interest in any kind of open-ended conflict in Syria,” adding, “We can take limited, tailored approaches, not getting drawn into a long conflict, not a repetition of, you know, Iraq, which I know a lot of people are worried about.” So, he does not intend to get involved in the messy business of the aftermath of whatever he decides to do—no nation-building, no siding with any side or faction in the fight. (And, by the way, I believe him on this: Obama is extremely resistant to the chutes and ladders of escalation.)

His objective, he stressed, is limited to restoring the “red line” he drew over chemical weapons, preserving the international norms. “[W]e do have to make sure,” he said, “that when countries breach international norms on weapons like chemical weapons … they are held accountable.”

OK, but what kind of attack accomplishes that objective—and no more? Here, Obama’s remarks on PBS are a bit disturbing: “If we are saying in a clear and decisive but very limited way, we send a shot across the bow, saying, ‘Stop doing this,’ that can have a positive impact on our national security over the long term … and may have a positive impact in the sense that chemical weapons are not used again on innocent civilians.” (Emphasis added.)

A “shot across the bow,” in military parlance, means a single shot, or a single volley of shots, to signal the opponent that you mean business and to test his response, to see if he backs down, before going on to the next step. If this really is what Obama plans to do, it isn’t enough. In fact, it’s worse than doing nothing. Shots across the bow generally don’t work. (I’m tempted to say they never work, but there’s bound to be an obscure exception or two in the annals of history.) It would be especially feckless in this case, given that Assad, looking out on the horizon, would see only a scattered few countries attacking him, a lot of those countries’ putative allies staying away, his own protectors (chiefly Iran and Russia) sticking by him, and his power base at home fairly stable.

To hold them truly accountable, to make sure they don’t use chemical weapons again, Obama has to do serious damage to the things Assad and his regime (chiefly his generals) hold dear. He needs to destroy as much of the military’s infrastructure as possible—air bases, weapons depots, command-and-control facilities (which, let’s face it, is often a euphemism for the leaders in the command-and-control facilities): everything. This will be harder than it might have been a few days ago, since U.S. officials have told the New York Times that they plan to attack such targets, as a result of which the Syrian officers have probably dispersed their weapons and emptied their headquarters so that the cruise missiles striking an air base will wreck fewer planes and those striking headquarters will kill many fewer commanders. As a result, the attack may have to be more extensive.

Obama says he doesn’t want to tilt the playing field in Syria’s civil war, but one thing any attack has to do is weaken Assad’s grasp on his country—or at least on his military. Secretary of State John Kerry said in his speech today that one effect of an attack should be to spur a negotiated solution to the civil war. The only way that will happen is if Assad or his henchmen realize that they are isolated. Supplies from Russia or Iran have to be severed. (Repeated attacks on airfields can help do that). More important, Assad needs to pick up a signal from Vladimir Putin that Moscow is not coming to his rescue. (This is how, eventually, Slobodan Milošević was dethroned in Serbia.)

It’s a thin line that Obama has to walk: launching a strike that’s sufficiently devastating to make Assad or his supporters (at home or abroad) tremble, but not so destructive that it kills lots of civilians or leaves behind a socio-economic catastrophe, which no one is likely to clean up and which therefore is bound to intensify the civil war.

Given the fragility and uncertainties, it would be good if this didn’t look like a purely American (or Western) assault, if more nations—especially Syria’s neighbors—came in on this, even with merely vocal support. One virtue of allies is that they can put a check on military excesses. This can prolong an operation, but it can also give it more international legitimacy.

The U.S. military in particular is a conservative organization. Most generals do not want to intervene in foreign wars, especially foreign civil wars, mainly because they know that they wind up holding the bag if things go south. If they do get pushed into drawing up a war plan, they tend to go overboard. They present a variety of options, placing a low probability of success on those that strike only a few targets (“a shot across the bow”) and a moderate-to-high probability of success only on those that strike practically everything. The president needs to question those options and the assumptions behind the probabilities so he doesn’t go too light or too heavy.

One thing worth noting: This is not Iraq. Some believed that Saddam Hussein wasdeveloping weapons of mass destruction. It is long known that Assad possesses them, and the evidence seems clear that he has used them with very deadly effect.

The first question is whether the rest of the world should do something about it. Obama’s case—that action is necessary to preserve the taboo against the use of chemical weapons—is the only case worth making, and I think the case is strong.

The second question, though, is whether the United States and maybe one or two other countries have the legitimacy to enforce international law on their own. That’s a tougher case to make.

The third question is whether President Obama and the allies he rallies have a plan that really accomplishes the strategic goal. At the moment that’s unclear. If other countries had signed on to the mission, they would be discussing that now. Maybe the very act of a dozen or so world leaders discussing a real war plan would have given Assad or Putin pause before the bombs dropped and the missiles flew.

As is, what happens next is a nail-biter. If the use of chemical weapons is still to be considered an international crime, and if members of the international community are to remain relevant actors in the prevention and punishment of those crimes, the answer cannot be that we do nothing—nor can it be that we fire a shot across the bow.

Fred Kaplan writes for Slate.