  Some years ago (Jackson and Dodgson 1997) analysis of the
angular-size/redshift relationship for ultra-compact radio sources indicted
that for spatially flat universes the best choice of cosmological parameters
was Omega_m=0.2 and Omega_Lambda=0.8. Here I present an astrophysical model of
these sources, based upon the idea that for those with redshift z>0.5 each
measured angular size corresponds to a single compact component which is moving
relativistically towards the observer; this model gives a reasonable account of
their behaviour as standard measuring rods. A new analysis of the original data
set (Gurvits 1994), taking into account possible selection effects which bias
against large objects, gives Omega_m=0.24+0.09/-0.07 for flat universes. The
data points match the corresponding theoretical curve very accurately out to
z~3, and there is clear and sustained indication of the switch from
acceleration to deceleration, which occurs at z=0.85.
