  Recently, it was shown that insertions of hadronic vacuum polarization at
O(alpha^4) generate non-negligible effects in the calculation of the anomalous
magnetic moment of the muon. This result raises the question if other hadronic
diagrams at this order might become relevant for the next round of g-2
measurements as well. In this note we show that a potentially enhanced such
contribution, hadronic light-by-light scattering in combination with electron
vacuum polarization, is already sufficiently suppressed.
