  In recent work, Gies and Karbstein have discovered that the two-loop
Euler-Heisenberg Lagrangians for scalar and spinor QED have non-vanishing
reducible contributions in addition to the well-studied irreducible ones. This
invalidates previous applications of those Lagrangians to the computation of
the two-loop $N$-photon amplitudes in the low energy limit. Here we compute the
corrections to those amplitudes due to the reducible contributions.
