  A dedicated test of the perturbative QCD NLO parton evolution in the very
small-$x$ region is performed. We find a good agreement with recent precision
HERA-data for $F_2^p(x,Q^2)$, as well as with the present determination of the
curvature of $F_2^p$. Characteristically, perturbative QCD evolutions result in
a positive curvature which increases as $x$ decreases. Future precision
measurements in the very small $x$-region, $x<10^{-4}$, could provide a
sensitive test of the range of validity of perturbative QCD
