To a growing number of Americans, Afghanistan is a festering pit where the United States has no vital interests. To a growing number of Afghans, the United States is a self-absorbed and feckless power that is playing games in their country.

Both caricatures are wrong. Yes, American troops should gradually withdraw from Afghanistan. And yes, the government of Afghan President Hamid Karzai remains corrupt and largely ineffective. But what is needed is a decisive agreement between the Afghan and American governments on the way forward, not sniping at each other in public and pandering to domestic political audiences.

First, let’s discard some myths:

Afghanistan is strategically unimportant to the United States: For even the most cynical Americans, a stable Afghanistan is important because of the roughly 100 nuclear warheads sitting in neighboring Pakistan. If hardline Taliban regain control of southern Afghanistan, it will be a safe haven for Pakistani Taliban and foreign militants. Attacks against Pakistan will definitely be plotted, and attacks on the United States could be planned from there as well.

All Afghans want Americans forces to leave immediately: The shameful video of Marines urinating on Taliban corpses, burning of Korans and massacre of 16 civilians will clearly increase the number of Afghans who want American soldiers out. In a November 2010 poll, 55 percent of Afghans said U.S. forces should withdraw immediately, but only 9 percent supported the Taliban. In some ways, there are two Afghanistans. The Taliban enjoy support in the rural south and east, but many Afghans – particularly the 23 percent who are city-dwellers and comparatively prosperous – fear that a post-American Afghanistan will quickly descend into civil war. They want the U.S. to help craft a political settlement before leaving. The violence today in Afghanistan is gruesome, but more Afghans died during the civil war of the 1990s.

An immediate American withdrawal will bring peace to Afghanistan: Michael Semple, an Afghanistan expert and longtime proponent of negotiating with the Taliban, argues that a hurried American withdrawal decreases the likelihood of reaching a negotiated agreement with the Taliban. “Any further acceleration would reduce the chances for a peace agreement,” he told me in an email, “and even increase the chances of a civil war.” If the Taliban think all U.S. forces are leaving in 2014, why would they come to the negotiating table and compromise now?

All Taliban are rabid fundamentalists uninterested in compromise: The decision by the Taliban’s leadership to negotiate with the U.S. was a controversial inside the group, according to Semple. Pragmatists supported it. Hawks opposed it. A political settlement in Afghanistan is the one way the Taliban can gain international acceptance and free themselves from the control of Pakistan’s intelligence service. That carrot is real; the United States should use it. Today’s “suspension” is a negotiating tactic. Talks will and should continue.

Accelerating the withdrawal of American troops is smart election year politics for Obama: A chaotic American withdrawal from Afghanistan will not help the president’s re-election effort. Stephen Biddle of the Council of Foreign Relations argues that Obama should maintain his current approach in Afghanistan and try to keep the country out of the news. “This is not a major political issue,” Biddle said in a conference call today with reporters. “The smartest approach is to be reasonable and centrist. Take the issue off the table.”

What should we do?

Hold steady: A mixed message is one of the things that has undermined Obama’s strategy in Afghanistan. He vastly increased American forces in 2009 but then announced they would leave in 18 months. The president says U.S. forces are withdrawing but is trying to negotiate a long-term agreement that will allow some American forces to remain in the country. The administration should adopt a clear message, stick to it and quietly look for an alternative to Karzai, who has promised to not run for re-election when his current term ends in 2014.

Deploy Afghans, not Americans: Most American forces should withdraw from Afghanistan by the end of 2014 as planned. But the U.S. should complete negotiations with the Afghan government to keep a residual force of 10,000 to 15,000 primarily Special Forces soldiers in the country to train Afghans and provide air support. The US and its NATO allies should guarantee at least five years of funding for Afghanistan’s now 350,000-strong security forces. A proposal to reduce the force to 230,000 should be rejected. The roughly $6 billion it will cost to fund Afghan forces annually is a fraction of the roughly $120 billion the U.S. spent in Afghanistan last year. Properly funded Afghan forces backed by U.S. Special Forces and air power can hold off the Taliban. The Taliban and their Pakistani backers can face stalemate through 2017 or negotiate.

Transfer Taliban commanders: The administration should transfer five Taliban commanders now held in Guantánamo Bay to house arrest in Qatar. The step will move forward talks with the Taliban and trigger a promised public statement from the group renouncing international terrorism and severing ties with Al Qaeda. If the Taliban fail to make the announcement or make other concessions, their unwillingness to compromise will be confirmed.

Pressure the Pakistani military: Guaranteeing the long-term funding of Afghan security forces and negotiating with pragmatic Taliban is the most effective way to pressure the Pakistani military to back a peace settlement. Pakistani army commanders must be convinced that the Taliban will not quickly triumph in a post-American Afghanistan. Instead, Pakistan will have a chaotic civil war, vast amounts of Afghan refugees and a Pakistani Taliban sanctuary on its border.

Afghanistan matters. Washington has cards to play. And there is still time for all sides to step back from the abyss of civil war.