  Context. Late O-type stars at luminosities $\log L/L_\odot \lesssim 5.2$ show
weak winds with mass-loss rates lower than 10$^{-8} M_\odot$ yr$^{-1}$. This
implies that their photospheric layers are not strongly affected by the stellar
wind. Aims. A hybrid non-local thermodynamic equilibrium (non-LTE) approach is
tested for analyses of late O-type stars. A sample of 20 mostly sharp-lined
Galactic O stars of spectral types O8 to O9.7 and luminosity classes V and IV,
previously studied in the literature using full non-LTE model atmospheres, is
investigated. Methods. Hydrostatic plane-parallel atmospheric structures and
synthetic spectra computed with Kurucz's Atlas12 code together with non-LTE
line-formation codes Detail and Surface, which account for the effects of
turbulent pressure on the atmosphere, were employed. High-resolution spectra
were analysed to derive atmospheric parameters and elemental abundances.
Fundamental stellar parameters were derived by considering stellar evolution
tracks and Gaia EDR3 parallaxes. Interstellar reddening was characterised by
fitting spectral energy distributions from the UV to the mid-IR. Results. A
high precision and accuracy is achieved for all derived parameters for 16
sample stars. Turbulent pressure effects turn out have significant effects.
Effective temperatures are determined to 1-3% uncertainty levels, surface
gravities to 0.05 to 0.10 dex, masses to better than 8%, radii to better than
10%, and luminosities to better than 20% uncertainty typically. Abundances for
C, N, O, Ne, Mg, Al, Si are derived with uncertainties of 0.05 to 0.10 dex and
for helium within 0.03 to 0.05 dex (1$\sigma$ standard deviations) in general.
Distances to the Lac OB1b association and to the open clusters NGC 2244, IC
1805, NGC 457, and IC 1396 are determined as a byproduct.
