  The dependency between the Gaussianity of the input distribution for the
additive white Gaussian noise (AWGN) channel and the gap-to-capacity is
discussed. We show that a set of particular approximations to the
Maxwell-Boltzmann (MB) distribution virtually closes most of the shaping gap.
We relate these symbol-level distributions to bit-level distributions, and
demonstrate that they correspond to keeping some of the amplitude bit-levels
uniform and independent of the others. Then we propose partial enumerative
sphere shaping (P-ESS) to realize such distributions in the probabilistic
amplitude shaping (PAS) framework. Simulations over the AWGN channel exhibit
that shaping 2 amplitude bits of 16-ASK have almost the same performance as
shaping 3 bits, which is 1.3 dB more power-efficient than uniform signaling at
a rate of 3 bit/symbol. In this way, required storage and computational
complexity of shaping are reduced by factors of 6 and 3, respectively.
