Kazakhstan's Kukushkin was eliminated by Spaniard Daniel Gimeno-Traver, who notched a 6-4, 3-6, 6-3 triumph at Bastad Tennis Stadium.
Italy's Volandri, meanwhile, knocked out the final Swede in the draw, wild card Michael Ryderstedt, in 6-4, 6-2 fashion.
Spanish stars David Ferrer and Nicolas Almagro are the top seeds at the event.
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