Over the years, to accommodate for increased speed of the game, the Axe Kick became more linear. It was chambered similar to a front kick, rather then executed with a straight leg. In addition, the kicking leg was brought up only 3 - 6 inches higher then the target.
For me personally, Axe kick worked well for "kicking on the motion" of my opponent. That is to kick on the opponents forward motion, but not necessarily waiting for them to kick.
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Windows Media: Axe Kick
Clip 1: 1996 World Cup
Clip 2: 1996 President Cup
Clips 3 &4: 1993: USTU (USAT) nationals