We use the 6C** sample to investigate the co-moving space density of powerful, steep- spectrum radio sources. This sample, consisting of 68 objects, has virtually complete K-band photometry and spectroscopic redshifts for 32 per cent of the sources. In order to find its complete redshift distribution, we develop a method of redshift estimation based on the K − z diagram of the 3CRR, 6CE, 6C* and 7CRS radio galaxies. Based on this method, we derive redshift probability density functions for all the optically identified sources in the 6C** sample. Using a combination of spectroscopic and es- timated redshifts, we select the most radio luminous sources in the sample. Their redshift distribution is then compared with the predictions of the radio luminosity function of Jarvis et al. We find that, within the uncertainties associated with the estimation method, the data are consistent with a constant co-moving space density of steep-spectrum radio sources beyond z > 2.5, and rule out a steep decline.