Stumbled across this one, and I'm so glad I did. Dr. Bajan, his website says,
 

comes from Leningrad, where the electric guitar and rock music once represented the only way he could distance himself from the [hyperbolic?] facade that was Soviet existence at the time. Even back then it was already clear that he had a soft spot for fast solos. After a while, the guitar wasn’t subversive enough for him and he turned – back to his roots – to the bajan, the accordion. A totally new perspective on his own musical tradition opened up for him. Up until then, the revolutionary anthems and Soviet pop hits of his musical environment provoked more eye-rolling than anything else, but now, exploring the roots of his musical heritage more deeply, he uncovered its connections to klezmer, jazz and folk music. Dr. Bajan drew on all of these influences – plus a hefty dose of rock’n roll – to create a totally original, contemporary new form: sovietabilly, music that conveys an intimate view of the dry-eyed and playful take of one post-Soviet cosmopolitan on life, the universe and groove. Balkan meets Charlie Parker in the kitchen of a Berlin walk-up flat, Manu Chao meets Odessa pentatonic. From the covers of Deep Purple right up through the much-loved “Kasatschoks” – whatever he touches is transformed in the blink of an eye into Dr. Bajan.
 

Sure, he sings like he's had more than enough vodka. It's big, raucous fun that proves you don't have to play polkas to get a party going with an accordion. His rock-folk mashup reminds me a bit of another Russian product, the band Limpopo.

Samples from the 2005 album Sovietabilly
Prinzessin auf der Erbse
Klezmer Hop
[mp3] Dr. Bajan: Früher In Leningrad
Samples from the 2006 album Fantasmagoria
Svetit No Ne Grejet
Pervomai
Hear more samples and find out more at Dr. Bajan's website.
Dr. Bajan on Youtube