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A broad range of scientific and industrial disciplines require precise optical measurements at very low light levels. Single-photon detectors combining high efficiency and high time resolution are pivotal in such experiments. By using relatively thick films of NbTiN (8-11\, nm) and improving the pattern fidelity of the nano-structure of the superconducting nanowire single-photon detectors (SNSPD), we fabricated devices demonstrating superior performance over all previously reported detectors in the combination of efficiency and time resolution. Our findings prove that small variations in the nanowire width, in the order of a few nanometers, can lead to a significant penalty on their temporal response. Addressing these issues, we consistently achieved high time resolution (best device 7.7\, ps, other devices 10-16\, ps) simultaneously with high system detection efficiencies () in the wavelength range of 780-1000\, nm, as …