  We prove that the knots and links that admit a 3-highly twisted irreducible
diagram with more than two twist regions are hyperbolic. This should be
compared with a result of Futer-Purcell for 6-highly twisted diagrams. While
their proof uses geometric methods our proof is achieved by showing that the
complements of such knots or links are unannular and atoroidal. This is done by
using a new approach involving an Euler characteristic argument.
