  We propose Four-Dimensional (4D) energy limit enumerative sphere shaping
(ESS) of $M$-QAM signaling to minimize rate loss and improve the transmission
performance over non-linear WDM optical-fiber systems. Simulation results show
that the proposed scheme outperforms the conventional ESS by
$0.19$~bit/4D-symbol in achievable information rate over a $205$-km single-span
link and a WDM transmission of five polarization-division-multiplexed channels
with $400$-Gbit/s net rate per channel. We also study the achieved performance
over several shaping block lengths and show that the achieved gains do not
scale well over multi-span systems.
