Bravo to Pope Francis, Angela Merkel and so many ordinary Germans and Austrians who have welcomed refugees into their lands. Kudos to those American politicians acknowledging that we should accept more Syrian refugees . the U.S. has admitted only 1,500 since the war started four years ago, which is pathetic.

If you have a heart, you’re moved by the refugees. But if you have a head, you also know that welcoming them in Germany won’t resolve the crisis.

There are 60 million people displaced worldwide, and more will now be willing to board flimsy boats to cross the sea.

“The trickle of refugees is only going to get bigger,” says Joshua Landis, a Syria expert at the University of Oklahoma. “Once people see that refugees are going to be taken in by the West, they’re going to stampede. This problem is going to metastasize.”

Unless we’re careful, the upshot could be more drowned toddlers.

As we inadvertently boost this tide of refugees, beneficiaries will include human smugglers and skinheads, neo-Nazis and far-right xenophobic politicians. An anti-immigrant party now leads the polls in Sweden, and Germany has reported 340 attacks on asylum seekers, including an apparent arson this week at a home sheltering them.

So by all means let’s respond with compassion to the refugees (not as jerks, as Hungarian officials have). But above all, let’s address the crisis at its roots, particularly in the Middle East.

One essential step is to improve conditions for the 3.7 million Syrian refugees in Lebanon, Turkey and Jordan. The World Food Program was just forced to cut 229,000 refugees in Jordan off food rations because it ran out of money, and if the world won’t pay for refugees to eat in Jordan, it will have to feed them in the West.

Then there’s the far more difficult task of trying to make Syria habitable again.

This may be impossible, but let’s be clear: As things stand, we’re on a trajectory for Syria to become even more horrific than it is now. Many experts expect the war to drag on for years, kill hundreds of thousands more people, and lead to an exodus of millions more refugees. We’re likely to see street-to-street fighting soon in Damascus, lifting the suffering and emigration to a new level.

I’m shaken by pleas I’ve seen from women in the besieged Syrian city of Zabadani, which for months has been surrounded by forces supporting the government. They fear that if the government forces take Zabadani, there will be massacres.

So hundreds of women in Zabadani have signed a statement calling for a cease-fire, international protection and evacuation of the wounded. They bravely use their names, despite the risk that they will be murdered or raped if the city falls.

“I’ve never been so depressed,” said Emile Hokayem, a Middle East analyst and author of a book on Syria. “There were options early on. But the options today are all costlier, riskier and come with lower returns.”

Yet as long as we’re talking about Syrian dysfunction, let’s also note European and American dysfunction. The Obama administration has repeatedly miscalculated on Syria and underestimated the problem, even as the crisis has steadily worsened. And some leading Republicans want to send in troops to confront the Islamic State (think Iraq redux).

The least bad option today is to create a no-fly zone in the south of Syria. This could be done on a shoestring, enforced by U.S. Navy ships in the Mediterranean firing missiles, without ground troops.

That would end barrel bombings. Just as important, the no-fly zone would create leverage to pressure the Syrian regime . and its Russian and Iranian backers . to negotiate.

“If they can’t use their aircraft, the day after they will know they can’t survive, and that will bring them to the table,” said Reza Afshar, a former British diplomat who now advises the Syrian opposition through his group, Independent Diplomat.

The aim of the talks, with no preconditions on either side, would be a cease-fire with a tweaking of boundary lines.

Look, this would be ugly. It would amount to a de facto partition of Syria and the partial survival of the regime, perhaps with a new Alawite general replacing President Bashar al-Assad. Yet otherwise we may be standing by as the slaughter spirals toward genocide.

Robert Ford, a former American ambassador to Syria who resigned because he found the Obama administration’s Syria policy indefensible, says a negotiation, even if successful, might drag on for two years as the carnage continued. Still, that’s better than the alternatives.

“It’s irresponsible to throw up our hands and say there’s nothing that can be done,” he added. “Then, almost certainly things will get worse.”