  I suggest that the beaming factor in bright ULXs varies as $b \propto \dot
m^{-2}$, where $\dot m$ is the Eddington ratio for accretion. This is required
by the observed universal $L_{\rm soft} \propto T^{-4}$ relation between
soft--excess luminosity and temperature, and is reasonable on general physical
grounds. The beam scaling means that all observable properties of bright ULXs
depend essentially only on the Eddington ratio $\dot m$, and that these systems
vary mainly because the beaming is sensitive to the Eddington ratio. This
suggests that bright ULXs are stellar--mass systems accreting at Eddington
ratios of order 10 -- 30, with beaming factors $b \ga 0.1$. Lower--luminosity
ULXs follow bolometric (not soft--excess) $L \sim T^4$ correlations and
probably represent {\it sub}--Eddington accretion on to black holes with masses
$\sim 10\msun$. High--mass X-ray binaries containing black holes or neutron
stars and undergoing rapid thermal-- or nuclear--timescale mass transfer are
excellent candidates for explaining both types. If the $b \propto \dot m^{-2}$
scaling for bright ULXs can be extrapolated to the Eddington ratios found in
SS433, some objects currently identified as AGN at modest redshifts might
actually be ULXs (`pseudoblazars'). This may explain cases where the active
source does not coincide with the centre of the host galaxy.
