We present optical spectroscopic data for a complete sample of 161 S5GHz≥0.2 Jy, flat-spectrum radio sources. The sources were observed as part of a survey for high-redshift, radio-loud quasars, and were selected for spectroscopic follow-up based on criteria of red optical colour and unresolved optical counterpart, as measured from APM scans of POSS-I plates. 13 objects from the spectroscopic sample were found to be radio-loud quasars with z> 3, of which two were previously known. We give positions, E (red) magnitudes, O ȒE colours, 5-GHz radio fluxes, radio spectral indices, optical spectra and redshifts where possible for the spectroscopic sample. We also give finding charts for the z > 3 QSOs. The highest redshift object found is a QSO with z = 4.30 (GB1508 + 5714, the subject of an earlier Letter). The sample also contains a z = 3.05 QSO, GB1759 + 7539, which is optically very luminous (E = 16.1). In addition, spectra are given for 18 S5GHz≥ 0.2 Jy, flat-spectrum radio sources that do not form part of the complete sample.