From a survey for the redshifted H i 21-cm and OH 18-cm absorption in the hosts of a sample of radio galaxies and quasars, we detect H i in three of the 10 and OH in none of the 14 sources for which useful data were obtained. As expected from our recent result, all of the 21-cm detections occur in sources with ultraviolet (UV) continuum luminosities of LUV≤ 1023 W Hz−1. At these ‘moderate’ luminosities, we also obtain four non-detections, although, as confirmed by the equipartition of detections between the type 1 and type 2 objects, this near-50 per cent detection rate cannot be attributed to unified schemes of active galactic nuclei (AGNs). All of our detections are at redshifts of z≲ 0.67, which, in conjunction with our faint source selection, biases against UV luminous objects. The importance of the UV luminosity (over AGN type) in the detection of the 21-cm absorption is further supported by the non-detections in the two high-redshift (z∼ 3.6–3.8) radio galaxies, which are both type 2 objects, while having LUV > 1023 W Hz−1. Our 21-cm detections in combination with those previously published give a total of eight (associated and intervening) H i-absorbing sources searched and undetected in OH. Using the detected 21-cm line strengths to normalize the limits, we find that only two of these eight sources may have been searched sufficiently deeply in OH, even though these are marginal.