The song Lystopad (November) was recorded when the Orange Revolution was at its peak.  It was the first song on the band's third album Perverziya, which was released a year later. The new album was recorded with the participation of Ukraine’s violin genius – Vasyl Heker, one of the disciples of folk double-bass play – Yuriy Barbenyuk, and cimbalom players Ivan Kavatsyuk and Volodymyr Polyovchyk. One month later, in January 2006, HAYDAMAKY signed a contract with German recording company EastBlok Music and the new album was re-released in Germany under the title Ukraine Calling.    
The new release was a milestone in the group’s history. HAYDAMAKY’s popularity skyrocketed. Collaboration with the concert agency Agents4music and later with La Candella resulted in the first wave of massive tours, presentations and interviews on Europe’s major TV channels, offers, invitations and flattering reviews.  A few weeks after the release, the album appeared at number seven on the World Music Chart Europe. In the meantime, the song Za Nashov Stodolov (Behind Our Barn) made its way onto Charley Gillet’s playlist, one of the BBC’s leading world music radio DJs, whose radio program The Sound of the World is broadcast all over the world. In October 2006, thanks to the album Ukraine Calling, the German label EastBlok Music broke into WOMEX’s top twenty for the Top Label Award 2006. HAYDAMAKY, whose creativity was so highly appreciated, participated in the award ceremony in Seville, Spain.  
Ukraine Calling or Perverziya was greatly inspired by the creativity of the post-modern Ukrainian writer Yuriy Andrukhovych. The very work was a tribute to the writer’s talent. In 2007, in addition to solo concerts in Ukraine and other European countries, the band participated in AmsterdamRootFest (Amsterdam, Netherlands), Mundial (Tilburg, Netherlands), Musicas do Mundo (Sines, Portugal), recorded two music videos for Kokhanya (Love) and Bozhestvena Trompita (Heavenly Trompita) directed by Taras Khymych.