  We present a global fit to HERA data on the reduced cross section measured in
electron-proton collisions in the region of small Bjorken-$x$: $x\le
x_0=10^{-2}$ and moderate to high values of the virtuality $Q^2<Q^2_{max}=650$
GeV$^2$. The main dynamical ingredients in the fits are two recently proposed
improved BK equations for the description of the small-$x$ evolution of the
dipole scattering amplitude. These two new equations provide an all-order
resummation of double collinear logarithms that arise beyond leading
logarithmic accuracy. We show that a very good description of data is possible
in both cases, provided the parent dipole or smallest dipole prescriptions are
employed for the running of the coupling.
