  Experimental studies of nuclear collisions involving light weakly-bound
nuclei show a systematic suppression of the complete fusion cross section by
$\sim$30\% with respect to the expectation for tightly bound nuclei, at
energies above the Coulomb barrier. Although it is widely accepted that the
phenomenon is related to the weak binding of these nuclei, the origin of this
suppression is not fully understood. In here, we present a novel approach that
provides the complete fusion for weakly bound nuclei and relates its
suppression to the competition between the different mechanisms contributing to
the reaction cross section. The method is applied to the $^{6,7}$Li+$^{209}$Bi
reactions, where we find that the suppression of complete fusion is mostly
caused by the flux associated with non-elastic breakup modes, such as the
partial capture of the projectile (incomplete fusion), whereas the elastic
breakup mode is found to play a minor role. Finally, we demonstrate that the
large $\alpha$ yields observed in these reactions can be naturally explained as
a consequence of a {\it Trojan Horse} mechanism.
