INCIRLIK AIR BASE, Turkey — Here’s a positive move by Turkey, a country that often seems to be heading in the wrong direction: Despite Ankara’s severe misgivings, it is allowing the U.S. military to fly daily bombing missions from here against the Islamic State — in support of a Syrian Kurdish militia called the YPG that Turkey regards as a terrorist threat.

Turkey offered the Incirlik base last year after a dozen years of tepid military relations with the United States, its superpower ally. Turkish President Recep Tayyip Erdogan is deservedly criticized for muzzling journalists and suppressing democracy, but on this issue he has allowed his military to behave responsibly.

I had a window on these Middle East machinations during a visit to Incirlik on Monday with Gen. Joseph Votel, the Centcom commander. It was the last stop on a tour of the region that included a secret U.S. training camp in northern Syria.

The U.S. military strategy against the Islamic State in Syria has increasingly relied on the battle-hardened fighters of the YPG, despite Ankara’s protests. The U.S. has grafted Sunni Arab forces with the Kurds, under the umbrella name of “Syrian Democratic Forces.” But as Votel explained, the U.S. must “go with what we’ve got,” which for now is mainly the YPG.

Votel told me in Syria that when he met two days later with Turkish officials in Ankara, he would credit them as “fabulous partners,” but would stress that “we have a very good partner on the ground” in the YPG, too. “Part of my job is to help balance this out,” he explained.

Gen. Yasar Guler, the deputy chief of the Turkish military, appears to have responded with similar nuance on Monday. According to the Turkish daily Hurriyet, he told the American general: “Do not be surprised if the YPG lets you down when the fight against [Islamic State] gets tough.” Guler reportedly also urged the U.S. to support Turkish-backed moderate Arab forces against the Islamic State in northern Syria, rather than relying so much on the Syrian Kurds.

The exchange illustrates how “the U.S. campaign has helped empower the Turkish military and increased the importance of military-to-military contacts,” argues Bulent Aliriza, who directs Turkey studies at the Center for Strategic and International Studies. Even as Erdogan has consolidated power, he has given the generals more space to resume cooperation with the U.S.

A vivid summary of the U.S. bombing campaign came from Air Force Col. Sean McCarthy, who commands a squadron of about a dozen A-10 “Warthog” ground-attack planes based here. He said his jets were operating over Syria 24/7, and that they were largely “autonomous” of the Turkish hosts. “We don’t discuss with them where we’re going,” he said, standing next to one of his planes.

Despite this wary military cooperation, U.S. strategy remains on a collision course with that of Turkey, a NATO ally. What can be done to prevent an eventual rupture that would damage all concerned? Here are two suggestions:

Turkey should explore a quiet dialogue with the political leadership of both the YPG and the Kurdistan Workers Party, or PKK, which Ankara claims (probably rightly) is the godfather of the Syrian Kurdish militia. Erdogan was making progress in discussions with the PKK until he reversed course last year. An understanding with the Kurds would enhance Erdogan’s legacy, Turkish security and regional stability.

America should consider modestly augmenting its proxy force in Syria with another Syrian Kurdish militia, the Rojava Peshmerga, that’s more acceptable to both Turkey and the official Syrian opposition in Geneva (which dislikes the YPG almost as much as Turkey does). The “Roj Pesh,” as it’s known, is backed and trained by the Kurdistan Regional Government in Iraq and its leader, President Massoud Barzani.

What could this additional Kurdish force provide? Possibly a bridge across what’s now a big gap in U.S. strategy. I talked by phone Thursday with Brig Gen. Mohammed Rejeb Dehdo, the commander of the Roj Pesh. He said he has 3,000 trained fighters based in Iraq ready to cooperate with the YPG under overall U.S. command. One sticking point is whether the command center would be in Zakho, controlled by the Barzanis, or in Sulaymaniyah, controlled by the rival Talabani clan. Surely that’s a solvable issue.

One U.S. commander privately describes the American campaign in Syria as “realpolitik on steroids.” OK, defeat the Islamic State now, worry about the regional mess later. But the U.S. and Turkey need to get smarter about regional strategy or they’re heading for a crackup.

David Ignatius’ email address is davidignatius@washpost.com.