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 \sim 3 , and there is clear and sustained indication of the switch from acceleration to deceleration , which occurs at z = 0.85 .