We present observations and analyses of seven Galactic O stars of type O6 and earlier. The analyses are carried out using NLTE plane-parallel, hydrostatic models as well as NLTE spherical models with mass-loss. With detailed calculations for the former and simulations for the latter, it is shown that the flux blocking due to UV metal lines is important for these objects, in agreement with previous studies, and the way the mechanism operates is explained. We find that the plane-parallel, hydrostatic unblanketed model atmospheres have increasing difficulties in fitting the early-type spectra of massive stars, and for 50 000 K and above a fit seems to be impossible. The gravities derived are relatively low even for the luminosity class V stars. These objects also show the mass discrepancy found in earlier studies, indicating that sphericity and mass-loss are important, even at their higher gravities. We then perform an analysis using spherical models with mass-loss. It is found that gravities should be increased by 0.1-0.25 dex, reducing, but not solving, the mass discrepancy. We show that spectroscopic masses are in better agreement with the theory of radiatively driven winds than evolutionary masses are. A helium abundance larger than solar is also obtained for most objects. Some additional effects (partly related to present approximations) that have an influence in our analyses are studied. It is found that He iI lambda 4200 is less sensitive to details of the model calculations than He iI lambda 4541 and thus it is preferred for temperature determinations, with the consequence of lower effective temperatures. It is shown that the fits to He iI lambda 4686 are improved when the upward rates of the He iI resonance lines are reduced (with respect to the conventional treatment adequate for lines formed in expanding atmospheres), either by setting them in detailed balance or by artificially adding extra opacity sources that simulate line blocking. The He iI blend with H_alpha ,is also affected. Some stars of our sample have such high mass-loss rates that the derivation of gravities from the wings of Balmer lines, in particular H_{log gamma}, becomes doubtful. For the most extreme objects, the mass-loss rates needed to fit H_alpha are different from those needed to fit H_{log gamma}, by a maximum factor of two. From the point of view of individual stars, we have analysed some of the most massive and luminous stars in the Milky Way. According to our analysis, three of them (Cyg OB2 #7, HD 15 570 and HD 15 558) have particularly large initial masses, close to or in excess of 100 M/Msunsun. Finally, the least luminous object in our sample, HD 5 689, could have been erroneously assigned to Cas OB7 and might be a runaway star. The INT is operated on the island of La Palma by the RGO in the Spanish Obervatorio de El Roque de los Muchachos of the Instituto de Astrof\'i sica de Canarias.