Aims. We analyse the spectral energy distributions (SEDs) of the most distant galaxies discovered with the Hubble Space telescope and from the COSMOS survey and determine their physical properties, such as stellar age and mass, dust attenuation, and star-formation rate. Methods. We use our SED fitting tool including the effects of nebular emission to analyse three samples of z ∼ 6−8 galaxies with observed magnitudes J AB ∼ 23 to 29. Our models cover a wide parameter space. Results. We find that the physical parameters of most galaxies cover a wide range of acceptable values. Stellar ages, in particular, are not strongly constrained, even for objects detected longward of the Balmer break. As already pointed out earlier, the effects of nebular lines significantly affect the age determinations of star-forming galaxies at z ∼ 6−8. We find no need for stellar populations with extreme metallicities or other non-standard assumptions (IMF, escape fraction) to explain the observed properties of faint z-dropout galaxies. Albeit with large uncertainties, our fit results show indications of dust attenuation in some of the z ≈ 6−8 galaxies, which have best-fit values of A V up to ∼1. Furthermore, we find a possible trend of increasing dust attenuation with galaxy mass, and a relatively large scatter in specific star-formation rates, SFR/M . Conclusions. The physical parameters of very high-z galaxies may be more uncertain than indicated by previous studies. Dust attenuation seems also to be present in some z ≈ 6−8 galaxies, and may be correlated with galaxy mass, as is also the case for SFR.