  In this note we consider higher-loop contributions to the planar dilatation
operator of N=4 SYM in the su(2) subsector of two complex scalar fields. We
investigate the constraints on the form of this object due to interactions of
two excitations in the BMN limit. We then consider two scenarios to uniquely
fix some higher-loop contributions: (i) Higher-loop integrability fixes the
dilatation generator up to at least four-loops. Among other results, this
allows to conjecture an all-loop expression for the energy in the near BMN
limit. (ii) The near plane-wave limit of string theory and the BMN
correspondence fix the dilatation generator up to three-loops. We comment on
the difference between both scenarios.
