  We reprove a necessary condition for the Sakuma-Weeks triangulation of a
2-bridge link complement to be minimal in terms of the mapping class describing
its alternating 4-string braid construction. For the 2-bridge links satisfying
this condition we construct explicit angle structures on the Sakuma-Weeks
triangulations and compute both multiplicative and additive lower bounds on the
complexity of the link complements via volume estimates. These lower bounds are
an improvement on existing volume estimates for the 2-bridge links examined.
