  I study the problem of renormalizing a non-renormalizable theory with a
reduced, eventually finite, set of independent couplings. The idea is to look
for special relations that express the coefficients of the irrelevant terms as
unique functions of a reduced set of independent couplings lambda, such that
the divergences are removed by means of field redefinitions plus
renormalization constants for the lambda's. I consider non-renormalizable
theories whose renormalizable subsector R is interacting and does not contain
relevant parameters. The "infinite" reduction is determined by i) perturbative
meromorphy around the free-field limit of R, or ii) analyticity around the
interacting fixed point of R. In general, prescriptions i) and ii) mutually
exclude each other. When the reduction is formulated using i), the number of
independent couplings remains finite or slowly grows together with the order of
the expansion. The growth is slow in the sense that a reasonably small set of
parameters is sufficient to make predictions up to very high orders. Instead,
in case ii) the number of couplings generically remains finite. The infinite
reduction is a tool to classify the irrelevant interactions and address the
problem of their physical selection.
