We report efficient single-photon detection (η = 20% at 1550 nm wavelength) with ultranarrow (20 and 30 nm wide) superconducting nanowires, which were shown to be more robust to constrictions and more responsive to 1550 nm wavelength photons than standard superconducting nanowire single-photon detectors, based on 90 nm wide nanowires. We also improved our understanding of the physics of superconducting nanowire avalanche photodetectors, which we used to increase the signal-to-noise ratio of ultranarrow-nanowire detectors by a factor of 4, thus relaxing the requirements on the read-out circuitry and making the devices suitable for a broader range of applications.