Channel geometry governs the unitary osmotic water channel permeability, pf, according to classical hydrodynamics. Yet, pf varies by several orders of magnitude for membrane channels with a constriction zone that is one water molecule in width and four to eight molecules in length. We show that both the pf of those channels and the diffusion coefficient of the single-file waters within them are determined by the number NH of residues in the channel wall that may form a hydrogen bond with the single-file waters. The logarithmic dependence of water diffusivity on NH is in line with the multiplicity of binding options at higher NH densities. We obtained high-precision pf values by (i) having measured the abundance of the reconstituted aquaporins in the vesicular membrane via fluorescence correlation spectroscopy and via high-speed atomic force microscopy, and (ii) having acquired the vesicular water efflux from scattered light intensities via our new adaptation of the Rayleigh-Gans-Debye equation.