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In footage of the performance on YouTube, Britney belted the song – appearing to sing without a backing track — while addressing male dancers sitting in chairs.
Brit's done a few covers over the years, including the Rolling Stones' "Satisfaction," but the Alanis track was a surprise on her "Circus" setlist.
Britney's tour continues on Tuesday in Detroit, Michigan, with a number of Midwest and West Coast dates still to come.
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