  The possibility of an improvement of current NLO Monte Carlo event generators
by means of choosing a suitable factorization scheme is studied. The optimal
factorization scheme for combining initial state parton showers and NLO hard
scattering cross-sections is the ZERO factorization scheme, in which all NLO
splitting functions vanish. However, it has turned out that the ZERO
factorization scheme has a limited range of practical applicability. Hence,
this paper is focused on searching for a factorization scheme which is
applicable at the NLO in the full range of x relevant for QCD phenomenology and
simultaneously close to the ZERO factorization scheme (i.e. the corresponding
NLO splitting functions are close to zero).
