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We present our studies on the quantum efficiency (QE) and the noise equivalent power (NEP) of the latest-generation, nanostructured, superconducting, single-photon detectors (SSPDs) in the wavelength range from 0.5 to 5.6 μm, operated at temperatures in the 2.0- to 4.2-K range. Our detectors are designed as 4-nm-thick and 100-nm-wide NbN meander-shaped stripes, patterned by electron-beam lithography and cover a 10×10-μm2 active area. The best-achieved QE at 2.0 K for 1.55-μm photons is 17%, and QE for 1.3-μm infrared photons reaches its saturation value of ∼30%. The SSPD NEP at 2.0 K is as low as 5×10-21 W/Hz-12/. Our nanostructured SSPDs, operated at 2.0 K, significantly outperform their semiconducting counterparts, and, together with their GHz counting rate and picosecond timing jitter, they are devices-of-choice for practical quantum key distribution systems and free-space (even interplanetary) quantum optical communications.