  Scattering amplitudes in QCD exhibit a definite RG flow with energy towards
the unitarity limit. In this paper we put forward an evolution equation which
allows one to modify continuously the pre-asymptotic RG flow towards
"saturation" of Wilson line correlators. It preserves the linearly unstable
zero field fixed point and the unitarity limit attractor. We present the
evolution equations in a form suitable for efficient numerical solution. Hence,
the proposed evolution equation in principle permits phenomenological
comparisons of our incorrect pre-asymptotic RG flows to the BK/JIMWLK flow of
QCD. Ultimately, it may lead to observational constraints on the approach to
unitarity, constraining it to be specifically the one of QCD. However, it
appears that single-inclusive particle spectra in the forward region of p+A
collisions at RHIC alone do not provide stringent constraints on the evolution.
