Washington ? A sign of Russia’s defensiveness, bordering on paranoia, is that some senior Russian officials regard the recent buzz about shale gas and oil as American propaganda designed to undermine Moscow’s clout as an energy producer.

Vladimir Putin’s Russia has a chip on its shoulder, for sure. It’s a big weight of resentment, reflecting the crushed ambitions of a fallen superpower. But Russia still has big shoulders, too. It’s a country that, for all its ills, has the ability to assist or obstruct U.S. diplomacy.

The administration is exploring ways to engage Russia as President Obama begins his second term. At the top of the list are the biggest U.S. headaches — Syria, Iran and North Korea. The White House thinks that after a period of frosty relations, Putin is also looking to rebuild a cooperative relationship.

White House officials are encouraged that even when relations were sour, Putin never threatened core U.S. interests, such as the “northern distribution route” for shipping supplies to U.S. and NATO forces in Afghanistan, transiting former Soviet states. “They want to find a way back to a stable relationship,” argues one senior official.

The outreach to Russia is meant to be hands-on, embodying Vice President Joe Biden’s dictum that “all politics is personal.” Biden expansively courted Russian Foreign Minister Sergey Lavrov on the sidelines of the Munich Security Conference this month. National security adviser Tom Donilon is planning a trip soon to Moscow to see Putin and discuss arms control and other issues. John Kerry, the new secretary of state, spoke with Lavrov last Sunday and is planning to meet him soon. And President Obama will probably meet Putin this September in Russia before the G-20 meeting.

Biden’s meeting with Lavrov on Feb. 2 illustrated the new bid for cooperation. Noting that Russia had trained the Syrian military unit that handles chemical weapons, he proposed that the U.S. and Russia cooperate in securing those weapons if President Bashar al-Assad’s regime should fall. It was an implicit recognition of Russia’s continuing interest in Syria after Assad is gone.

Biden and Lavrov also discussed the danger that the war in Syria could produce a Balkanized nation fragmented into ethnic cantons. Russia understands that such an outcome would harm its interests.

The diplomatic contribution Russia could make in Syria was highlighted that same day in Munich, when Lavrov met Sheik Ahmad Moaz al-Khatib, who leads a coalition of Syrian opposition groups. Afterward, Lavrov praised Khatib’s willingness to meet with representatives of the Assad regime and promised continued Russian contact with the Syrian opposition.

When Kerry phoned Lavrov Sunday, “they discussed the importance of the U.S. and Russia using their respective influence on the parties in support of a viable political transition process,” according to the State Department.

While these diplomatic maneuvers are encouraging, they are faint sparks of light against the dark tableau of Russian support for Assad in a war that has now killed more than 60,000 Syrians. Part of the frustration of dealing with Putin is that for him, everything seems to be transactional. There’s a price for Russian peacemaking in Syria or support for limiting Iran’s nuclear program. But what is it? Obama might make the deal, if he knew what it was.

Critics of Obama’s policy argue that engaging Putin will only encourage him to continue his repressive policies at home. Putin is a bully, goes this argument, and appeasing him will backfire. He encourages Assad’s brutal war in Syria because he fought similar battles against Chechen rebels. And as the U.S. engages Putin, it becomes complicit in his suppression of dissent. 

So what’s the answer to this classic foreign-policy dilemma, where U.S. interests and values are in conflict? I’d argue that the benefits of a more cooperative U.S.-Russian relationship — on Syria, Iran, North Korea, arms control and other issues — are so substantial that they are worth the cost. That’s a heavy burden, especially since it’s likely to be borne by Russian human-rights activists.

The Obama administration made a similar strategic choice in its first term, when it decided that a positive “reset” with Russia was a top priority and placed missile defense, NATO expansion and other issues lower on its list. This decision opened the way for Russian support of U.N. resolutions sanctioning Iran.

A second presidential term isn’t a clean slate, but it offers a new chance to test whether Russia’s interests and America’s can be aligned. To get where he wants over the next four years, Obama needs to unlock the Russia door.