  We present a detailed study of the subtle interplay transpiring at the level
of two integral equations that are instrumental for the dynamical generation of
a gluon mass in pure Yang-Mills theories. The main novelty is the joint
treatment of the Schwinger-Dyson equation governing the infrared behaviour of
the gluon propagator and of the integral equation that controls the formation
of massless bound-state excitations, whose inclusion is instrumental for
obtaining massive solutions from the former equation. The self-consistency of
the entire approach imposes the requirement of using a single value for the
gauge coupling entering in the two key equations; its fulfillment depends
crucially on the details of the three-gluon vertex, which contributes to both
of them, but with different weight. In particular, the characteristic
suppression of this vertex at intermediate and low energies enables the
convergence of the iteration procedure to a single gauge coupling, whose value
is reasonably close to that extracted from related lattice simulations.
