We reinvestigate Kreimer's Hopf algebra structure of perturbative quantum f
ield theories with a special emphasis on overlapping divergences. Kreimer f
irst disentangles overlapping divergences into a linear combination of disj
oint and nested ones and then tackles that linear combination by the Hopf a
lgebra operations. We present a formulation where the Hopf algebra operatio
ns are directly defined on any type of divergence. We explain the precise r
elation to Kreimer's Hopf algebra and obtain thereby a characterization of
their primitive elements.