  We prove peeling estimates for the small data solutions of the Maxwell Klein
Gordon equations with non-zero charge and with a non-compactly supported scalar
field, in $(3+1)$ dimensions. We obtain the same decay rates as in an earlier
work by Lindblad and Sterbenz, but giving a simpler proof. In particular we
dispense with the fractional Morawetz estimates for the electromagnetic field,
as well as certain space-time estimates. In the case that the scalar field is
compactly supported we can avoid fractional Morawetz estimates for the scalar
field as well. All of our estimates are carried out using the double null
foliation and in a gauge invariant manner.
