  It is known that the colored Jones polynomial of a $+$-adequate link has a
well-defined tail consisting of stable coefficients, and that the coefficients
of the tail carry geometric and topological information on the $+$-adequate
link complement. We show that a power series similar to the tail of the colored
Jones polynomial for $+$-adequate links can be defined for $all$ links, and
that it is trivial if and only if the link is non $+$-adequate.
