Despite some of Donald Trump's conciliatory campaign rhetoric toward Russia, there is little optimism in Moscow over the prospects for a reversal in the dismal downward spiral of US-Russia relations.

Like many observers of the US president-elect, Russian foreign policy experts see Mr. Trump as a black box, and have no idea what his worked-out Russia policy might look like – if it exists at all.

And they harbor deep skepticism that the US under any president would agree to sit down with a Russian leader to change a US-Russia relationship currently tested all around the world in a variety of situations. They include dueling military exercises in Eastern Europe; the mutual economic slugfest of sanctions and countersanctions sparked by Russia's annexation of Crimea; an escalating war of words between government officials; and Syria, where forces of the two sides are engaged at what are sometimes cross-purposes, creating a risk of deadly miscalculation.

Even Vladimir Putin, welcoming Trump's electoral victory over the hawkish Hillary Clinton, warned that restoring goodwill in a relationship perhaps more antagonistic than it was in the cold war would be a "long and difficult path."

But were the two sides to move beyond the angry froth that dominates the headlines, Russian analysts say a US-Russia "grand bargain" on a few key geopolitical areas could begin to shape a more stable post-cold war order.

The Middle East

There are some signs that Trump is already gravitating toward the long-held Russian view that peace in Syria will require at least temporary consolidation of the Bashar al-Assad regime to defeat the armed jihadist-dominated rebellion and restore central government rule.

The Russians have never denied that Mr. Assad is a brutal dictator, but they have argued that he is committed to secular values, presents no threat to the West, and would cooperate in cracking down on terrorism. They insist that the alternative is chaos or, worse, the emergence of another extreme Islamist state.

Trump told the New York Times last week that "I have a different view on Syria than everybody else," which some understand to mean ending efforts at regime change in Syria and teaming up with Russia to combat the Islamic State. Such a deal might finally enable Russia and the US to jointly sponsor a permanent settlement for that long-suffering country.

But "even if Trump proves to be more cooperative, it will still be a difficult job to bring all the diverse actors in Syria to the bargaining table," says Irina Zvyagelskaya, an expert with the official Institute of Oriental Studies in Moscow. "You have the Assad regime, Iran, and Hezbollah on one side, with many different rebel groups backed by Turkey and the Gulf States on the other. It's a nightmare. But maybe the US and Russia, seriously working together, could do it."

And were that effort to succeed, it could hypothetically lead to further US-Russian cooperation to address the broader crisis in the Middle East.

"The current, collapsing order in the region is the deferred consequence of big power meddling in the region a century ago, and there is evidently a need for superpower intervention now to fix it," says Viktor Kremeniuk, deputy director of the official Institute of USA-Canada Studies in Moscow. "It might involve redrawing some maps to produce a settlement that could be stable and lasting. That can't happen without Washington and Moscow working together."

The former Soviet Union

Since the collapse of the USSR a quarter century ago, there has been a scramble for influence amid the shards of that wrecked empire, while a resurgent Russia has tried to put some of the pieces back together by forming its own military and economic unions.

The main bone of contention between Russia and the US today is Ukraine, where a pro-Western street revolt overthrew a Moscow-friendly president almost three years ago, leading the Kremlin to annex the Russian-populated Crimean peninsula and back a bloody anti-Kiev insurrection in Ukraine's east.

Finding a route to peace in Ukraine would be critical to any lasting East-West detente, but the Minsk II accords negotiated between Moscow and European powers has so far failed dismally while the crisis threatens to erupt again into hot war between Kiev and the rebellious eastern regions at almost any time.

Some Russian analysts say that the tension might be relieved by removing Moscow's deepest fear – that Ukraine could join NATO – from the table. They suggest that a big power deal similar to the cold war treaty that guaranteed Austria's independence in return for it accepting the status of a neutral buffer zone between East and West, or the similar arrangement over Finland, might work well for Ukraine.

"The idea of Ukraine or Georgia joining NATO is a red line for Russia. It would bring troops of an adversarial alliance to within a few hours march of Moscow, and it would never be accepted here," says Sergei Strokan, foreign affairs columnist for the Moscow daily Kommersant. "While NATO has repeatedly postponed Ukraine's membership, it has never renounced the possibility. Doing so formally could create the basis for a far more rational discussion and eventual settlement of the crisis in Ukraine."

The chief sticking point would be Crimea, which the West regards as aggression and illegal annexation by Russia of Ukraine's sovereign territory. Trump, referring to polls that show Crimeans overwhelmingly satisfied with the transfer, has hinted that he might be willing to recognize it.

But that might not be acceptable to Western foreign policy establishments, at least not without some major quid pro quo from Russia. Though Russian analysts decline to discuss this idea on the record, Trump might consider offering to trade acknowledgement of Russia's Crimea annexation for the Kremlin's recognition of Kosovo's independence, granted – Russia claims illegally – by NATO powers after wresting the territory from sovereign Serbia in a 1999 war.

Security in Europe

A constant complaint from Russian foreign policymakers has been that, following the collapse of the USSR, no new security system was designed for Europe that might include Russia as an equal partner. Thus, they say, Russia was condemned to remain on the outside looking in as the West expanded its institutions, primarily NATO and the European Union, into the former Soviet zone.

Some Russians suggest there should be a new "Yalta Conference," an allusion to the World War II summit that designed the post-war order, to create a more inclusive security architecture for Europe and the world.

Short of that, they argue, there should be urgent discussions about curbing the military buildup in Europe and especially placing limits on US-led plans to install a missile defense system in Europe that Moscow fears will erode its nuclear deterrent. European leaders, led by Germany, have recently talked about holding their own arms control negotiations with Russia, which could change the entire complexion of this issue.

"Any talks about missile defense and Europe's security system will be very complex and difficult, but they become more necessary with each passing day," says Sergei Markov, a former adviser to Putin. "We hear that Trump wants to build a stronger US military. We don't object to that, but we are concerned about Russia's own security. We'd want a deal in which increased US security doesn't decrease ours."

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Mr. Kremeniuk says the most important thing Putin and Trump could do in their first meeting is to set some ground rules and define terms of discussion.

"The whole East-West dialogue has become so poisonous lately that it will not be easy to move the conversation to a constructive level," he says. "Before discussing problems, a critical precondition for any success is to first reestablish the atmosphere of civil discourse between Russia and the US."