  The Yukawa couplings of the simpler models of D-branes on toroidal
orientifolds suffer from the so-called ``rank one'' problem -- there is only a
single non-zero mass and no mixing. We consider the one-loop contribution of
E2-instantons to Yukawa couplings on intersecting D6-branes, and show that they
can solve the rank one problem. In addition they have the potential to provide
a geometric explanation for the hierarchies observed in the Yukawa coupling. In
order to do this we provide the necessary quantities for instanton calculus in
this class of background.
