We present new models for the X-ray photoevaporation of circumstellar discs which suggest that the resulting mass loss (occurring mainly over the radial range 10-40 AU) may be the dominant dispersal mechanism for gas around low mass pre-main sequence stars, contrary to the conclusions of previous workers. Our models combine use of the MOCASSIN Monte Carlo radiative transfer code and a self-consistent solution of the hydrostatic structure of the irradiated disc. We estimate the resulting photoevaporation rates assuming sonic outflow at the surface where the gas temperature equals the local escape temperature and derive mass loss rates of ~10^{-9} M_sun/yr, typically a factor 2-10 times lower than the corresponding rates in our previous work (Ercolano et al., 2008) where we did not adjust the density structure of the irradiated disc. The somewhat lower rates, and the fact that mass loss is concentrated towards slightly smaller radii, result from the puffing up of the heated disc at a few AU which partially screens the disc at tens of AU. (.....) We highlight the fact that X-ray photoevaporation has two generic advantages for disc dispersal compared with photoevaporation by extreme ultraviolet (EUV) photons that are only modestly beyond the Lyman limit: the demonstrably large X-ray fluxes of young stars even after they have lost their discs and the fact that X-rays are effective at penetrating much larger columns of material close to the star (abridged).
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