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According to Sloan's official website, the band's name refers to a friend's nickname.

Their friend Jason Larsen was called Slow One by his French-speaking boss, which with the French accent sounded more like Sloan.

The original agreement was that they could name the band after their friend's nickname as long as he was on the cover of their first album.

As a result, it is Larsen who appears on the cover of the Peppermint EP.