What does "clean as a whistle" mean?

Completely, entirely, thoroughly, as in He chopped off the branch, clean as a whistle. The allusion in this simile is unclear. It may have been a replacement for the 18th-century clear as a whistle, which alluded to the pure, clean sound of a whistle (it has few overtones). However, it was adopted to describe something thoroughly done. [Early 1800s]