  We solve for the structure of a hot accretion disc with unsaturated thermal
Comptonisation of soft photons and with advection, generalizing the classical
model of Shapiro et al. The upper limit on the accretion rate due to advection
constrains the luminosity to $\simless 0.15 y^{3/5} \alpha^{7/5}$ of the
Eddington limit, where $y$ and $\alpha$ are the Compton and viscosity
parameters, respectively. The characteristic temperature and Thomson optical
depth of the inner flow at accretion rates within an order of magnitude of that
upper limit are $\sim 10^9$ K and $\sim 1$, respectively. The resulting spectra
are then in close agreement with the X-ray and soft \g-ray spectra from
black-hole binaries in the hard state and Seyferts. At low accretion rates,
bremsstrahlung becomes the dominant radiative process.
