Two quark propagators with different analytic structure are employed i
n Bethe-Salpeter type equations for the pion and scalar diquark form f
actors. One of the quark propagators has been calculated with the incl
usion of a trivial (bare) quark-gluon vertex and, as a consequence, co
ntains a complex conjugate pair of logarithmic branch points. The othe
r quark propagator is obtained using a non-trivial (dressed) vertex an
satz and is entire, with an essential singularity at infinity. The eff
ects of these different quark propagators on the BSE solutions are com
pared.