  The extreme degrees of the colored Jones polynomial of any link are bounded
in terms of concrete data from any link diagram. It is known that these bounds
are sharp for semi-adequate diagrams. One of the goals of this paper is to show
the converse; if the bounds are sharp then the diagram is semi-adequate. As a
result, we use colored Jones link polynomials to extract an invariant that
detects semi-adequate links and discuss some applications.
