We present results of an ongoing project dedicated to reassess the shape of the radial abundance gradient of O in the Milky Way based on deep spectroscopy of H II regions. Most of he data have been obtained with spectrographs attached to 8-10 m telescopes. The actual sample comprises 35 objects located at Galactocentric distances, R_{G}, from 5.1 to 17 kpc, covering a substantial fraction of the Galactic disc. We determine {\elect} from the direct method for all of the objects, implying that the abundance determinations are very reliable. We confirm the absence of flattening of the O gradient in the outer Milky Way beyond R_{25}, at least up to R_{G} ˜ 17 kpc. We report the presence of a flattening or drop of the O abundance in the inner part of the Galactic disc, at R_{G} < 7-8 kpc. Finally, we find that the scatter of the O abundances of H II regions with respect to the gradient fitting is not substantially larger than the observational uncertainties, indicating that O is well mixed in the interstellar gas along the observed section of the Galactic disc.