The attempts by Hillary Clinton’s campaign to paint Donald Trump as the candidate of President Vladimir Putin has led to an intense search for the Republican nominee’s Russian connections. Not much has turned up. But Russian oligarchs are among the Clinton campaign donors.

As of today, Trump’s links to Russia are tenuous. His adviser Carter Page once worked for the natural gas giant Gazprom. His campaign manager Paul Manafort once worked for the deposed Ukrainian president, Viktor Yanukovych, who is often described as pro-Russian even though he spent most of his career trying to set Russia and the European Union against each other. Manafort also had unsuccessful dealings with a Russian billionaire, Oleg Deripaska, who is still trying to recover millions of dollars from him. Trump himself once sold a very expensive house in Florida to Dmitri Rybolovlev, who made billions selling Russian potash. “I mean I do that,” Trump said on ABC on Sunday. “I have lots of condos.”

No prominent Russian-Americans have surfaced among Trump’s donors. Even Leonard Blavatnik, the owner of Warner Music, who made most of his fortune — estimated by Bloomberg Billionaires at $16.2 billion — in Russia in oil and other industrial assets and who sprinkled donations generously among Republican candidates, has not given anything to Trump. His wife, Emily, has pitched in $33,400 to the Democratic Party and the maximum for a personal contribution, $2,700, to Clinton.

Two other Clinton donors are Maria Baibakova, who gave $2,700 and who was described by Politico as a “big player in Democratic Party politics,” hosting fundraisers and serving on policy committee, and Daria Zhukova, with the same contributions as Emily Blavatnik’s.

Baibakova is the daughter of Oleg Baibakov, a close associate of Mikhail Prokhorov, the owner of the Brooklyn Nets and a dwindling number of Russian assets. The sketchy privatization of Norilsk Nickel, the world’s biggest palladium producer, made Prokhorov rich; Baibakov served as vice president of Norilsk Nickel and then ran the development arm of Prokhorov’s Russian investment vehicle, Onexim. Prokhorov has recently been in trouble with the Kremlin because of sensitive investigations published by a newspaper he owns. Baibakov is apolitical. “Doing politics in our country is not just boring and unsafe, it’s pointless,” he once said in an interview. So anyone looking for a Putin trail here will be disappointed.

Maria Baibakova, however, drew ridicule in Russia for a callous column in the local edition of Tatler magazine on how to treat household help. She warned, for example, against handing over old clothes to staff. The piece caused a storm on social networks and Baibakova was forced to apologize: “The text is heavily edited and when I translate it to English I can see it is insensitive and crude.” Russian is her mother tongue, though, and it’s not clear why the English translation might be needed.

Zhukova’s connections to Putin are somewhat murkier. She is the wife of Roman Abramovich, whose $10.7 billion fortune is based on the sale of his majority interest in the oil company Sibneft to Gazprom — at a price that many considered inflated at the time.

To avoid the kind of frontal attack Putin inflicted on the billionaire Mikhail Khodorkovsky, Abramovich played nice with Putin, serving for more than seven years as governor of the remote region of Chukotka and funding the post from his own pocket. Abramovich still owns a significant asset in Russia — a stake in the steelmaker Evraz.

Zhukova, a major figure in the contemporary art world, runs a big art center in Moscow called the Garage. That makes Abramovich, who spends most of his time outside Russia, politically vulnerable and requires him to remain a Putin ally. He still has influence: He’s credited with helping Sergei Sobyanin become the mayor of Moscow, for example.

Zhukova, like Baibakova, is a U.S. citizen. That doesn’t change the origin of her money — and a certain lack of sensitivity to things that Americans may find offensive. In 2014, she was photographed sitting on a chair in the shape of a bound black woman. An online fashion publication released the photo on Martin Luther King’s birthday. Zhukova apologized, saying the chair was merely an art object and that she “abhorred” racism.

There’s nothing wrong with these wealthy Russians’ affinity for Clinton: Both Baibakova and Zhukova profess to hold progressive views. Yet it’s easy to imagine the uproar if they were Trump supporters. A Democratic-leaning pundits would rush to point out a Kremlin connection.

Looking for “Russian connections” in the U.S. election is a ridiculous exercise. Putin doesn’t have the ability to influence the outcome of the election, and while he has reasons to prefer Trump, who is going out of his way to promise a detente with Russia, it would be imprudent of him not to be wary of both candidates. Yet the connections are everywhere: Russian money is essentially global, no matter what its origin. The world has changed since the locked-down Soviet Union was America’s arch-enemy.

Leonid Bershidsky is a Berlin-based writer and Bloomberg View columnist.