  Important corrections to BFKL evolution are obtained from non-leading
contributions and from non-linear effects due to unitarisation or saturation.
It has been difficult to estimate the relative importance of these effects, as
NLO effects are most easily accounted for in momentum space while unitarisation
and saturation are easier in transverse coordinate space. An essential
component of the NLO contributions is due to energy conservation effects, and
in this paper we present a model for implementing such effects together with
saturation in Mueller's dipole evolution formalism. We find that energy
conservation severely dampens the small-x rise of the gluon density and, as a
consequence, the onset of saturation is delayed. Using a simple model for the
proton we obtain a reasonable qualitative description of the x-dependence of F2
at low Q^2 as measured at HERA even without saturation effects. We also give
qualitative descriptions of the energy dependence of the cross section for
gamma*-gamma* and gamma*-nucleus scattering.
