Over the last year, Mr. Grebenshikov has been allowed to record with Western musicians in England and the United States, and he offered a preview of his album "Radio Silence" (scheduled for release in June) on Saturday night at the Bottom Line.

With the help of the Eurythmics’ David Stewart, who produced the album and played in the band Saturday, Mr. Grebenshikov has moved toward mainstream Anglo-American rock.

The dissonances are gone, most of the new lyrics are in English and only a few songs use Slavic-sounding minor keys. Mr. Grebenshikov’s husky voice recalls Bob Dylan, Lou Reed and their British disciples, from David Bowie to Mark Knopfler of Dire Straits, along with John Lennon. (One song, "Fields of My Love," is a near-remake of the Beatles’ "All You Need Is Love.") He’s fluent in English, with only a slight accent, and his lyrics still take free-associative leaps.

In the late set, it was easy to see the stage presence that drew Soviet listeners to unofficial concerts. Mr. Grebenshikov sings with grit and authority; even a handful of songs in Russian conveyed dramatic urgency across the language barrier. But his individuality was nearly submerged by his band.

Busily dispensing its chugging, internationally negotiable rock riffs, it didn’t leave much breathing room for Mr. Grebenshikov’s voice; female backup singers completed the cover-up. Perhaps it was simply a bad sound mix and an overeager band, but the music seemed designed to make Mr. Grebenshikov sound like one more standard-issue rocker. After he’s crossed so many barriers, now is the time to flaunt his nonconformity.