We use three samples ( 3CRR , 6CE and 6C* ) selected at low radio frequency to constrain the cosmic evolution in the radio luminosity function ( RLF ) for the ‘ most luminous ’ steep-spectrum radio sources . Although intrinsically rare , such sources give the largest possible baseline in redshift for the complete flux-density-limited samples currently available . Using parametric models to describe the RLF which incorporate distributions in radio spectral shape and linear size as well as the usual luminosity and redshift , we find that the data are consistent with a constant comoving space density between z \sim 2.5 and z \sim 4.5 . We find this model is favoured over a model with similar evolutionary behaviour to that of optically-selected quasars ( i.e . a roughly Gaussian distribution in redshift ) with a probability ratio of \sim 25 : 1 and \sim 100 : 1 for spatially-flat cosmologies with \Omega _ { \Lambda } = 0 and \Omega _ { \Lambda } = 0.7 respectively . Within the uncertainties , this evolutionary behaviour may be reconciled with the shallow decline preferred for the comoving space density of flat-spectrum sources by Dunlop & Peacock ( 1990 ) and Jarvis & Rawlings ( 2000 ) , in line with the expectations of Unified Schemes .