The United States has spent the past two years struggling to craft a policy to weaken Syrian president Bashar Assad and Al Qaeda-linked militants at the same time. Now, as President Barack Obama seeks to strip Syria of its chemical weapons, it’s time for Washington to build ties to those inside Syria who are committed to the same anti-Assad and anti-jihadist goals: the Kurds.

Many Kurds in Syria, for decades oppressed and marginalized by the regime, oppose both Assad and the jihadists. They have championed reshaping Syria into a democratic state that can protect their rights. They have expanded their hold over the traditionally Kurdish region of north and northeast Syria bordering Turkey and Iraq. In the process, the Kurds have built up fledgling and secular local governing institutions.

Just as importantly, the Kurds are actively fighting Al Qaeda-linked militants from Jabhat al-Nusra and the Islamic State in Iraq and Syria. In late August, following months of intermittent clashes, Kurdish fighters from the Democratic Union Party (PYD), the largest and most powerful of the dozen or so Kurdish political groups inside Syria, launched a counter attack against the jihadists. The Kurds killed tens of jihadists of Jabhat al-Nusra, Al Qaeda’s Syrian arm. Clashes with armed Islamist groups continue.

Kurdish opposition to Islamic radicals isn’t a temporary phenomenon. Kurds in Syria—like those throughout the region—oppose political Islam and its vision of an Islamic state. Kurdish nationalist groups like the PYD are secular nationalists, and they understand that there’s nothing to be gained from striking a deal with jihadists. That’s not necessarily the case with the Syrian Arab opposition, something that worries the United States. In fact, the PYD’s leader, Salih Muslim, has called jihadist groups the common enemy of the United States and the Kurds, and has said he wants contact with Washington.

Given the convergence of strategic interests, why is Washington ignoring the Kurds?

Pressure from regional allies is partly to blame. Turkey is wary of Syrian Kurdish demands for autonomy because it fears the effect on Kurds inside Turkey. Ankara also is unhappy about the PYD’s ties to the Kurdistan Workers Party (PKK), the Kurdish rebels who have been fighting for self-rule in Turkey for the last thirty years. The PYD, for all its disclaimers, is a PKK offshoot. This means that any win for the PYD is also a victory for the PKK.

Syrian opposition forces are also suspicious of the Kurds. The Syrian National Coalition, the U.S.-supported umbrella group for anti-Assad forces, from the outset refused to accept Kurdish demands for self-rule in a post-Assad state. While the Coalition moderated its position this summer, Kurds remain suspicious and the PYD has continued to shun the Syrian opposition. Meanwhile, the Free Syrian Army, itself a mixed bag of different anti-Assad rebels and rebel factions, has clashed intermittently with the PYD.

Building ties to the PYD gives the Obama administration a reliable ally—and determined fighting force—when it comes to disrupting jihadist groups from their goal of controlling Syria. Reaching out to the PYD also makes long-term sense. Regardless of what happens in Syria, the PYD will dominate Kurdish politics there. Better it does this as an ally of the United States, giving Washington some sway.

The PYD needs Washington in more ways than it realizes. The group, like its patron the PKK, is autocratic, erratic, and inexperienced when it comes to democratic institutions and practices. This may not matter (or may even help) when running an illegal, armed rebellion, but for a group seeking international acceptance for Kurdish autonomy within Syria, this must change. The United States can demand commitment to democratic pluralism and human-rights norms as a requisite for ties.

Opening a formal channel of communication with the PYD also gives the United States a back door to the PKK, something Washington needs as long as the PKK remains on the U.S. and European terrorism lists. There’s little reason to hold back. Ankara’s doing the same. Earlier this year, the Turkish government opened talks with the PKK’s imprisoned leader Abdullah Ocalan to negotiate an end to the rebel war.

The PKK, which initially agreed to withdraw its forces as a goodwill gesture, said in September it was halting the withdrawal because Turkey hasn’t reciprocated with any democratic changes. The reforms proposed by Turkish prime minister Recep Tayyip Erdogan this week have already been dismissed by the PKK as not meeting basic demands. A new breakout of fighting won’t be good for stability in Turkey or in the region. All the more reason for the United States to give itself a conduit to the PKK through the PYD.

Turkey is already hedging its bets in Syria. The PYD’s Salih Muslim has been to Turkey at least twice since July. Ankara pressed him to join the formal Syrian opposition, something Muslim has so far refused to do, citing the Syrian opposition’s antagonism to Kurdish autonomy.

Opening contacts with the PYD will also mitigate Kurdish suspicions of the United States, given its ties to Turkey and its focus on strengthening the Syrian Arab opposition. It will also help dissipate Kurdish fears that any U.S. strike will give Turkish troops the chance to cross the border and occupy the Kurdish region.

The Obama administration has made a willingness to engage one of its hallmarks. If it applies this approach to the Kurds of Syria, it could find that what’s good for the Kurds may also be good for Washington.

Aliza Marcus, a writer based in Washington D.C., is the author of “Blood and Belief: The PKK and the Kurdish Fight for Independence.”