  We present a theoretical model that fully supports the recently disclosed
generalized droop formula (GDF) for calculating the signal-to-noise ratio (SNR)
of constant-output power (COP) amplified dispersion-uncompensated coherent
links operated at very low SNR. We compare the GDF to the better known Gaussian
noise (GN) model. A key finding is that the end-to-end model underlying the GDF
is a concatenation of per-span first-order regular perturbation (RP1) models
with end-span power renormalization. This fact allows the GDF to well reproduce
the SNR of highly nonlinear systems, well beyond the RP1 limit underlying the
GN model. The GDF is successfully extended to the case where the
bandwidth/modes of the COP amplifiers are not entirely filled by the
transmitted multiplex. Finally, the GDF is extended to constant-gain (CG)
amplifier chains and is shown to improve on known GN models of highly nonlinear
propagation with CG amplifiers.
