Last September, Congress played an important role in deflecting U.S. military action in Syria, paving the way for a diplomatic solution that is destroying Syria’s chemical weapons. Today, bipartisan leaders of the Senate Foreign Relations Committee lament the Obama administration’s “lack of strategy” to end the spreading violence. Yet, as the “Geneva 2” peace conference looms, the critics are not offering an alternative policy.

This is too bad since the administration’s current approach to Geneva 2 ignores the lessons of recent history and risks sabotaging its estimable goal of seeking a political solution.

Despite the reigning pessimism on Syria, it is worth recalling that, over the past two decades, political negotiations have ended comparably bloody conflicts in Burundi, Cambodia, Democratic Republic of the Congo, El Salvador, Mozambique and Sudan. In all these countries the combatants pragmatically negotiated new political systems after they became mired in costly military stalemates with no foreseeable prospects for victory. External powers, including the United States, played critical mediating roles and used leverage (including economic sanctions, military and aid withdrawals, diplomacy and financial incentives) to propel the negotiations forward. Similar circumstances exist or are rapidly developing in Syria. And while that country poses some special problems, such as an extremely divided opposition, there is no reason to believe they are insurmountable. In Burundi, Cambodia and Congo multiple armed groups were either brought into settlements or defeated.

Yet in the run-up to Geneva 2, the administration appears to have paid scant attention to these successes and how they were achieved. In their public statements, top officials have focused almost exclusively on a single objective for the conference: the formation, by “mutual consent” of the Government and Opposition, of a Transitional Governing Body with “full executive powers” in which “[Syrian President Bashar al-] Assad and his close associates with blood on their hands will have no role  . . . ”

In contrast, when transitional governments were created in Burundi, Cambodia, Congo and Sudan, their authority was closely linked to detailed agreements by the opposing parties on what the country was transitioning to. These included specific provisions on matters such as army reform, constitution-writing, political party recognition, election reform, human rights protection, cease-fire and troop demobilization, the insertion of U.N. or regional peacekeeping forces, foreign relations and economic reform. It’s simply not logical for combatants to relinquish real power to a transitional government unless they know where it will be taking them. Yet the administration’s proposed TGB floats alone.

Furthermore, there is a wide disjuncture between the administration’s requirement for Assad’s summary ouster and the present situation in Syria. While there can be no doubt that a politically viable and stable Syria is impossible so long as the Assad regime remains in power, the Opposition Coalition has only managed to achieve a stalemate. Furthermore, any abrupt dismissal of Assad would amplify his supporters’ fears of annihilation by their increasingly sectarian foes. Meanwhile, Assad’s main external backers, Russia and Iran, do not perceive an alternative vehicle for assuring their interests. Hence the U.S. and its allies’ demand for Assad’s exclusion from the TGB is a non-starter.

The U.S. needs to revise its plan. Learning from recent history, it should focus first on working with Russia and Iran to persuade the opposing parties that their only realistic alternative is to negotiate the establishment of a pluralistic, representative, accountable political system that will protect all religious and ethnic groups and be buttressed by support from international peacekeeping forces and reconstruction assistance. Such a system could not possibly be an “Assad regime” even in the unlikely event that the now ex-dictator chose to participate in it and was allowed to do so.

The payoff to Russia and Iran for helping deliver Assad’s acquiescence for the new inclusive system would be twofold: (1) the creation of a firmer barrier to the spread of Sunni Islamic extremism and (2) an international precedent against violent, Western-sponsored regime change. The former interest is strongly shared by the U.S. and such major allies as Britain, France, Turkey, Jordan and Israel.

Once an agreement was reached on the major details of Syria’s political future, the issue of Assad’s role in the TGB would become less consequential and could be resolved in a number of ways. Considering the exceptional brutality of the Syrian government’s repression, it is quite possible that Syrian negotiators would exclude Assad from the TGB. On the other hand, they might very well wish to approach the problem in a different fashion to guarantee cooperation from the regime’s military, other state institutions and substantial constituency. Here, too, they might draw some inspiration from past experience, adapting it to Syrian realities.

For example, in Cambodia, the peace agreement created a “Supreme National Council” composed of key leaders from the government and opposition groups, but required that it delegate its power to the U.N. Transitional Authority, which ran a vast peacekeeping operation. In Burundi, leadership of the TGB was entrusted first to the current president and subsequently to the head of the main armed opposition group. In Congo and Sudan, rebel leaders were allocated high government positions.

If you want to ease out a destabilizing dictator, but are unwilling to mount the military intervention necessary to accomplish it, shouting at him to go is no solution. To effectively advance a political solution at Geneva 2, the Obama administration should plunge into the long, hard slog of mobilizing broad international support for a full-fledged, negotiated settlement. Therein lies the only hope for ending the suffering of the Syrian people and their neighbors and for halting the spread of violent extremism across the region. Congressional foreign policy leaders should once again be showing the way.

Stephen R. Weissman is the former staff director of the House Foreign Affairs Subcommittee on Africa.