Abstract: We present our studies on quantum efficiency (QE), dark counts, and noise equivalent power (NEP) of the latest generation of nanostructured NbN superconducting single-photon detectors (SSPDs) operated at 2.0 K. Our SSPDs are based on 4 nm-thick NbN films, patterned by electron beam lithography as highly-uniform 100÷120-nm-wide meander-shaped stripes, covering the total area of 10x10 μm² with the meander filling factor of 0.7. Advances in the fabrication process and low-temperature operation lead to QE as high as  30-40% for visible-light photons (0.56 μm wavelength)-the saturation value, limited by optical absorption of the NbN film. For 1.55 μm photons, QE was  20% and decreased exponentially with the wavelength reaching  0.02% at the 5-μm wavelength. Being operated at 2.0-K temperature the SSPDs revealed an exponential decrease of the dark count rate, what along with the high QE, resulted in the NEP as low as 5x10^-21 W/Hz^-1/2, the lowest value ever reported for near-infrared optical detectors. The SSPD counting rate was measured to be above 1 GHz with the pulse-to-pulse jitter below 20 ps. Our nanostructured NbN SSPDs operated at 2.0 K significantly outperform their semiconducting counterparts and find practical applications ranging from noninvasive testing of CMOS VLSI integrated circuits to ultrafast quantum communications and quantum cryptography.