Many properties of the superconducting state of high-T(c) materials ha
ve been interpreted within the Eliashberg framework with a very large
coupling (lambda greater-than-or-equal-to 3). Here we point out that t
he inclusion of non-adiabatic corrections acts as an effective couplin
g for various properties that can, therefore, be reproduced with a muc
h smaller coupling (lambda almost-equal-to 1) within the generalized t
heory. This can provide a new perspective for the analysis of supercon
ductivity data with moderate couplings but within a theory that goes b
eyond Migdal's theorem.