Having in mind the capacity optimization of power-constrained submarine links, by following the work in [1] we first compare the achievable information rate (AIR) of gain-flattened and un-flattened blocks of N b ≤ 12 spans with span loss 16.5dB and with end-span single-stage co-pumped erbium-doped fiber amplifiers (EDFA) when the transmitted wavelength division multiplexed (WDM) channels all have the same transmitted power. All EDFAs have the same pump power and the same physical parameters. In the flattened case, each EDFA is followed by an ideal gain-flattening filter (GFF) that chops off the EDFA gain exceeding the span loss. No GFFs are used in the un-flattended case. We show that, for block length Nb > 7, at large-enough input power the AIR of the GFF block exceeds that of the no-GFF block, while for Nb ≤ 7 at large input power the AIR is about the same. We next build a long submarine link by concatenating the Nb-span no-GFF blocks, and placing a GFF at the last EDFA of each block in order to flatten the block gain down to the Nb-span loss, and calculate the AIR of the resulting sparse-GFF submarine link, accounting also for nonlinear interference. For the 287-span case-study link with span loss 9.5dB used in [5], [9], we show that the best power efficiency is achieved by blocks of size Nb = 6 (i.e., one GFF every 6 spans) when the pump is around 12 mW. When the GFF excess loss is 0.3dB the top-AIR gain over the standard all GFF system is 9.5%, a value that decreases to 4% when the excess loss is zero. Considering that modern submarine-grade GFFs have almost zero excess loss, and that the most efficient pump power is likely too low to operate with, we conclude that sparse-GFF links offer little advantage in practice over the current design.