  We pursue the analysis of a set of generalized DGMLY sum rules for the
electromagnetic chiral parameters at order $e^2p^2$ and discuss implications
for effective Lagrangians with resonances. We exploit a formalism in which
charge spurions are introduced and treated as sources. We show that no
inconsistency arises from anomalies up to quadratic order in the spurions. We
focus on the sum rules associated with QCD 4-point correlators which were not
analyzed in detail before. Convergence properties of the sum rules are deduced
from a general analysis of the form of the counterterms in the presence of
electromagnetic spurions. Following the approach in which vector and
axial-vector resonances are described with antisymmetric tensor fields and have
a chiral order, we show that the convergence constraints are violated at chiral
order four and can be satisfied by introducing a set of terms of order six. The
relevant couplings get completely and uniquely determined from a set of
generalized Weinberg sum-rule relations. An update on the corrections to
Dashen's low-energy theorem is given.
