The Islamic State's defeat in Raqqa, Syria, this week is an important milestone in America's war to destroy that brutal terrorist organization.

Yet, it would be a mistake to declare "Mission Accomplished." To bring about the Islamic State's lasting defeat, the U.S. must act with urgent and ruthless dispatch on both the military and political fronts.

The goal is to win a war. That means finishing off the enemy — killing it. It also means leaving behind an environment in which peace is possible.

On the military track, President Trump made an important change from the Obama administration when he announced he would grant wide operational latitude to his commanders. Obama always made the commanders operate under time limits and politically prescribed troop levels, which hamstrung them and ensured that they could not be successful. Trump gave them the difficult, but nevertheless straightforward, task of ending the war. And he then gave them the tools and time they needed to achieve that blessed end.

Trump must continue to grant that flexibility so that the American military and our allies can maintain momentum in attacking Islamic State forces further down the Euphrates River valley. In eastern Syria, the U.S. should support fighters from local Sunni-Arab tribes in compressing Islamic State forces and limiting their freedom of movement. If we do so, combined with U.S. and allied air power, the coalition will further degrade Islamic State command and control capabilities and encourage desertions.

Recent history has shown us, however, that whenever we defeat an enemy in the Arab world, a hundred new problems flare up. In this case, we need to worry about Syria's regime expanding its assault on Syria's people, as well as half-dozen other sectarian fights. Military force may or may not be called for in addressing these issues. Diplomacy and shrewd politics will certainly be needed.

In Baghdad, the Trump administration must now ramp up its political support for Prime Minister Haider al-Abadi's embattled government. As the Islamic State grows weaker, Iran will exert increasing pressure on al-Abadi, and its attempts to ensure Sunni and Kurdish political blocs are second-tier players in Iraq's political future. If Iran gets its way, it will plant the seed of a terrorist successor to the Islamic State.

We can be grimly confident of this risk because it's already happened before. By 2010, America, Iraq, and Britain had annihilated Abu Musab al-Zarqawi's al Qaeda in Iraq. But when former President Barack Obama, for cynical political reasons, withdrew U.S. forces from Iraq in late 2011, Iranian Shiite-sectarian paranoia and influence came to define then-Prime Minister Nouri al-Maliki. Attacking and alienating Sunni civilians, the Iraqi government fueled the rise of the Islamic State and precipitated America's return to conflict.

Trump must not make the same mistake. While we should realistically accept that Iran will play a role in Iraqi politics, efforts to counter Iranian malevolence in Baghdad must be given economic, military, and intelligence priority.

America owes Iraq help to provide stability, because we helped create today's chaos by overthrowing Saddam Hussein, a dictator who, for moral if not for geopolitical reasons, needed to be removed from power.

But let's be clear; the Trump strategy need not mean American soldiers and Marines returning to Iraqi streets to fight with Shiite militias. Instead, Trump should follow America's 2009-2011 diplomatic effort in Baghdad. In those short golden years, American representatives were able to win the trust of Iraqi officials and influence them towards greater political consensus. For a moment, Iraq seemed destined for a stable, multisectarian democratic future.

In all this, Trump must decide whether he wishes to learn from previous American mistakes. Just as the Bush administration's grave error in Iraq was its three-year military failure to recognize a sectarian insurgency, the Obama administration's grave failure was its withdrawal of American political influence. Looking forward toward the Islamic State's destruction, Trump must also plant the seeds for a messy, but somewhat stable status quo in both Syria and Iraq.