On Approaching the Ultimate Limits of Communication Using a Photon-Counting DetectorCoherent states achieve the Holevo capacity of a pure-loss channel when paired with an optimal measurement, but a physical realization of this measurement scheme is as of yet unknown, and it is also likely to be of high complexity. In this paper, we focus on the photon-counting measurement and study the photon and dimensional efficiencies attainable with modulations over classical- and nonclassical-state alphabets. We analyze two binary modulation architectures that improve upon the dimensional versus photon efficiency tradeoff achievable with the state-of-the-art coherent-state on-off keying modulation. We show that at high photon efficiency these architectures achieve an efficiency tradeoff that differs from the best possible tradeoff--determined by the Holevo capacity--by only a constant factor. The first architecture we analyze is a coherent-state transmitter that relies on feedback from the receiver to control the transmitted energy. The second architecture uses a single-photon number-state source.