  We present a new approach to the consistent subtraction of a non
power-counting renormalizable extension of the Abelian Higgs-Kibble (HK) model
supplemented by a dim.6 derivative-dependent operator controlled by the
parameter $z$. A field-theoretic representation of the physical Higgs scalar by
a gauge-invariant variable is used in order to formulate the theory by
exploiting a novel differential equation, controlling the dependence of the
quantized theory on $z$. These results pave the way to the consistent
subtraction by a finite number of physical parameters of some
non-power-counting renormalizable models possibly of direct relevance to the
study of the Higgs potential at the LHC.
