  We compute the two-loop fermion self-energy in massless reduced quantum
electrodynamics (RQED) for an arbitrary gauge in the case where the photon
field is three-dimensional and the fermion field two-dimensional:
super-renormalizable RQED$_{3,2}$ with $N_F$ fermions. We find that the theory
is infrared finite at two-loop and that finite corrections to the fermion
propagator have a remarkably simple form.
