  It is shown that a large class of systems of non-linear wave equations, based
on the good-bad-ugly model, admit formal solutions with polyhomogeneous
expansions near null infinity. A particular set of variables is introduced
which allows us to write the Einstein field equations in generalized harmonic
gauge as a good-bad-ugly system and the functional form of the first few orders
in such an expansion is found by applying the aforementioned result. Exploiting
these formal expansions of the metric components, the peeling property of the
Weyl tensor is revisited. The question addressed is whether or not the use of
generalized harmonic gauge, by itself, causes a violation of peeling. Working
in harmonic gauge, it is found that log-terms that prevent the Weyl tensor from
peeling do appear. The impact of gauge source functions and constraint
additions on the peeling property is then considered. Finally, the special
interplay between gauge and constraint addition, as well as its influence on
the asymptotic system and the decay of each of the metric components, is
exploited to find a particular gauge which suppresses this specific type of
log-term to arbitrarily high order.
