  We analyse two new versions of \theta-expanded non-commutative quantum
electrodynamics up to first order in \theta and first loop order. In the first
version we expand the bosonic sector using the Seiberg-Witten map, leaving the
fermions unexpanded. In the second version we leave both bosons and fermions
unexpanded. The analysis shows that the Seiberg-Witten map is a field
redefinition at first order in \theta. However, at higher order in \theta the
Seiberg-Witten map cannot be regarded as a field redefinition. We find that the
initial action of any \theta-expanded massless non-commutative QED must include
one extra term proportional to \theta which we identify by loop calculations.
