  We study near-alternating links whose diagrams satisfy conditions generalized
from the notion of semi-adequate links. We extend many of the results known for
adequate knots relating their colored Jones polynomials to the topology of
essential surfaces and the hyperbolic volume of their complements: we show that
the Strong Slope Conjecture is true for near-alternating knots with spanning
Jones surfaces, their colored Jones polynomials admit stable coefficients, and
the stable coefficients provide two-sided bounds on the volume of the knot
complement. We also discuss extensions of these results to their Murasugi sums
and a class of highly twisted links.
