  Over-then-Under (OU) tangles are oriented tangles whose strands travel
through all of their over crossings before any under crossings. In this paper
we discuss the idea of gliding: an algorithm by which any tangle diagram could
be brought to OU form. Unfortunately, the algorithm is flawed. However, by
analyzing cases in which it does succeed we obtain a braid classification
result, which we also extend to virtual braids, and provide a Mathematica
implementation. We discuss other instances of successful "gliding ideas" which
appear in the literature - sometimes in disguise - such as the Drinfel'd double
construction, Enriquez's work on quantization of Lie bialgebras, and Audoux and
Meilhan's classification of welded homotopy links,
