We have used the SEST 15-metre and Onsala 20-metre telescopes to perform deep
(r.m.s. >~ 30 mJy) integrations of various molecular rotational transitions
towards damped Lyman-alpha absorption systems (DLAs) known to occult
millimetre-loud quasars. We have observed 6 new systems and improved the
existing limits for 11 transitions. These limits may be approaching the
sensitivities required to detect new systems and we present a small number of
candidate systems which we believe warrant further observation.Comment: 7 pages, 1 PS figure, 4 tables. Accepted by A&