Ukraine has a propaganda problem. Nearly every day, dozens of Russian news outlets spin a story about the rise of fascism in the embattled country, despite the collapse of the far right at the ballot box.

“Ukraine needs to do direct marketing to convince the world we’re not—as the Russians claim—a failed state,” Vasyl Myroshnychenko—an organizer at the Ukraine Crisis Media Center—told The Atlantic.

The Kremlin spends a lot of time and money manipulating the media. Following Pres. Vladimir Putin’s re-election in 2012, the Kremlin culled independent news outlets, created sweeping blacklists of Internet sites deemed subversive, launched a campaign targeting non-governmental organizations—all the while expelling outspoken foreign journalists.

For foreign audiences, Moscow spends hundreds of millions of dollars per year on English-language propaganda in the hope that it can control, or at least shape, any story Russia is involved in. The government has even organized online trolling in the comment sections of The Guardian.

This is—to put bluntly—all part of a broader strategy by the Kremlin to expand Russia’s sphere of influence using both hard and soft power.

Faced with such a campaign, what chance does a broke and relatively tiny country like Ukraine have at winning a media war? It turns out, a pretty good one.

To a certain extent, the Internet has leveled the playing field. Now that Ukraine has elected a government—its citizens are mobilizing in new ways. Crowdsourcing, independent news blogs and new media agencies are taking on Moscow’s media empire and winning.

However, a sympathetic ear in the West won’t save Ukraine or bail out its economy when Russia turns the screws. There’s also a risk Ukraine’s success could lead to a presumption among Ukrainians that Western governments support them more than they actually do.