As recently as February, President Obama was signaling that the United States might withdraw all of its military forces from Afghanistan at the end of this year.

Whether that so-called zero option was truly under consideration or was simply a tactic to obtain President Hamid Karzai’s signature on a bilateral security agreement, Obama made it clear last week that several thousand U.S. military personnel will remain in the country in 2015. That assumes Karzai’s successor will sign the agreement, and both presidential candidates in next month’s election have indicated that they would.

Those are welcome developments, and Obama’s plan represents a responsible way to draw down America’s presence in that country.

Americans are understandably weary of the U.S. military engagement in Afghanistan, which has lasted for more than a decade and cost the lives of more than 2,300 Americans — without extirpating the Taliban or purging Afghan politics of cronyism and corruption. But there also have been accomplishments: in the professionalization of Afghan forces, in progress toward a stronger civil society and in the education and empowerment of women.

The original justification for sending U.S. forces to Afghanistan was to end its use as a staging ground for attacks on Americans by al-Qaida, not to engage in nation-building. But having overthrown the Taliban, the U.S. and its allies rightly saw it as their responsibility to try to undo the effects of that fanatical regime’s misrule. The residual force Obama plans could play an important role in consolidating the progress already achieved — by training Afghan forces and engaging in limited counter-terrorism operations.

Under the plan, U.S. forces in Afghanistan will decline from the current 32,800 to 9,800 by the beginning of 2015 and will fall to half that number by the end of next year. By the end of 2016, the U.S. military presence will shrink to a size comparable to that of the U.S. security contingent in Iraq.

Are these the optimal numbers for a successful transition to a situation in which the government in Kabul can deal with security on its own? No one can be sure, but the force levels seem reasonable and so does the assumption that most of the remaining U.S. forces won’t be in harm’s way. (American fatalities have declined sharply in the last two years.) Republicans are criticizing Obama for announcing a date for the withdrawal of most the residual force, but a deadline will concentrate the minds of the Afghans on the importance of improving their own readiness.

Afghanistan remains a country with a weak central government, endemic corruption, ethnic tensions and a continuing insurgency. There is no guarantee that the longer goodbye Obama announced last week will enable Afghans to surmount those and other obstacles to a peaceful and productive society. But the effort is worth making.