Initially, the Taliban agreed only that it would not attack major population centers, but U.S. negotiators pushed for a more comprehensive cessation of violence.

The Taliban have now agreed not to attack population centers, highways and government institutions, with some exceptions (that’s why it is not a full cease-fire). One of those exceptions: They have retained the right to attack if they believe government convoys are using the period of calm to supply areas otherwise out of their reach.

There was less certainty among officials on what reduced hostilities might look like in the next phase of the peace process: the negotiations between the Afghan sides after the United States and the Taliban sign their deal.

One senior Afghan official briefed on the discussions said the expectation was that after the one-week test period, there should not be a return to more attacks, and that the situation will perhaps even more closely resemble a cease-fire.

But other officials said that the Americans might apply a less strict gauge during what will probably be a long period of negotiation between Afghans, and that they might be willing to put up with a certain amount of violence as long as it is significantly reduced from the current levels. (Over the past year, the insurgents have carried out anywhere between 50 to 90 attacks a day.)

Still, there will be deterrents against the Taliban stepping up attacks after reaching a deal with the United States. Among them: U.S. negotiators are likely to reserve the right to come to the help of Afghan forces with air power.

Some are expressing an ambitious hope: that when the two Afghan sides do begin talks, they will agree on a formal cease-fire right away. To date, the Taliban have resisted that, fearing that a cease-fire could break their ranks. Many of their commanders have been unhappy with what they see as their political leaders giving in to shifting U.S. demands that they fear are a trap to weaken them on the battlefield. But if they secure a deal for a U.S. withdrawal, the Taliban’s commanders might become more amenable.