  We introduce a novel sign-dependent metric: the energy dispersion index (EDI)
of sequences that endured chromatic dispersion, denoted as D-EDI, which
exhibits a more accurate opposite variations with the transmission performance
compared to the standard EDI metric. Then, by applying D-EDI and EDI to the
sequence selection (SS) process, %with enumerative sphere shaping (ESS) for
$M$-QAM signaling, we present two signaling approaches denoted as D-SS and E-SS
respectively. These approaches are designed to minimize rate loss and enhance
transmission performance in nonlinear optical fiber transmission systems,
catering to both short-distance and long-haul scenarios. With enumerative
sphere shaping (ESS) as distribution matcher (DM), our simulation results
reveal significant performance gains over ESS without sequence selection (SS),
with improvements up to $0.4$~bits/4D-symbol. These improvements were observed
over a $205$-km single-span standard single mode fiber link in WDM
transmission, with five dual-polarization channels, each operating at a net
rate of $400$~Gbit/s. Furthermore, we demonstrate that D-SS surpasses ESS
without SS by $0.03$~bits/4D-symbol in achievable information rate over a
$30\times80$~km link in a single-wavelength, with 8 discrete multi-band (DMB)
transmission, and an $880$~Gbit/s net rate. Notably, our proposed D-SS scheme
achieves similar performance to a sequence selection based on a full split-step
Fourier method (SSFM) simulation and it consistently delivers throughput
enhancements across various block lengths and selected sequence lengths.
