  We show that in arbitrary even dimension, the two-loop scalar QED
Heisenberg-Euler effective action can be reduced to simple one-loop quantities,
using just algebraic manipulations, when the constant background field
satisfies F^2 = -f^2 I, which in four dimensions coincides with the condition
for self-duality, or definite helicity. This result relies on new recursion
relations between two-loop and one-loop diagrams, with background field
propagators. It also yields an explicit form of the renormalized two-loop
effective action in a general constant background field in two dimensions.
