The head of the Syrian opposition says he’s going to Geneva for the next round of U.S.-Russian-sponsored peace talks Monday, even though the opposition rejects any future role for President Bashar Assad, whose regime will be the other party in the talks.

The Syria diplomacy might be described as “the art of the impossible,” borrowing from the title of a collection of speeches by the former Czech President Vaclav Havel, who helped negotiate the transition from communism to democracy in Eastern Europe. Similar impossibilities confront the peacemaking being attempted by U.S. Secretary of State John Kerry and his Russian counterpart, Foreign Minister Sergey Lavrov.

The Syria peace train should have derailed weeks ago. The parties don’t agree on any major issue – they won’t even sit down with each other in the same room – and the sponsors, Russia and America, remain rivals more than partners. Yet the locomotive keeps on chugging up the hill – largely because the alternative would be a disastrous plunge into the abyss of even deeper sectarian war.

Riyad Hijab, the Syrian former prime minister who heads the opposition steering group known as the High Negotiations Committee outlined his positions in a telephone interview with me Friday. His key demand is a formula that removes Assad from power soon and instead gives authority to a transitional body. This is precisely the issue the United States and Russia had hoped to finesse by deferring the question of Assad’s future until after elections take place, in theory 18 months from now.

“We want a transitional body with full authority,” Hijab insisted. He said this would be his message to Staffan de Mistura, the United Nation’s special envoy for Syria, when the negotiations convene in Geneva today. The Geneva meeting will feature what are known as “proximity talks,” with the two sides talking separately to the mediator, but not to each other.

Hijab said that attacks by Assad’s regime against the rebels have lessened, but they haven’t ended, under the shaky cease-fire that has taken effect since last month. “The war hasn’t stopped, but the rate of violence is less,” he said. Although some analysts have predicted that the talks will ultimately produce a federal Syria, Hijab said he rejected such as outcome because it would be “the starting point to divide Syria.” He said this position was a “red line” for the opposition group that he heads. “We support more decentralization, so local authorities have more power, but no federalism. Federalism will divide the whole area” into mini-states, to the benefit of Iran, he argued.

Given the impasse on big negotiating issues, some leaders in the Syrian opposition argue that the United States should concentrate on smaller steps that would build support for the moderate opposition and weaken the hold of the extremists from Daesh (ISIS) and the Nusra Front. Opposition leaders have urged the administration, for example, to force the Syrian president to allow humanitarian relief for the besieged town of Daraya, which is located in the northwest suburbs of Damascus. Gaining help for Daraya would bolster the U.S.-backed opposition’s standing among Syrians, the leaders have argued.

Rebel leaders also urge the United States to encourage non-governmental organizations to rush humanitarian supplies to areas in northwest Syria, near the cities of Aleppo and Idlib, where the Nusra Front had been strong but may be weakening. As the extremists lose local support, it is argued, the United States should quickly help moderate groups so that they may fill the vacuum.

The hardest problem for the opposition, now as for the past four years, has been that the key outside powers have differing agendas. The United States backs the Syrian Kurdish group known as the YPG, even though it is the deadly enemy of Turkey, a NATO ally. The Kurds in recent weeks have been cleverly playing off the U.S. and the Russians, further complicating the Syrian campaign.

The biggest surprise about Syria diplomacy isn’t its success – there’s still precious little of that – but that it continues at all. That’s due chiefly to the persistence of Kerry and his team – and the exhaustion of the combatants.