This article explores a universal issue in higher education: how in practice can we secure the most productive relationships between the research universities pursue and the education they provide? It opens by drawing from three recent international literature reviews summarising research on research-teaching links, sometimes termed a 'nexus'. It then proceeds inductively to analyse grounded empirical data from practitioners in an English post-1992 University. This data describes "what" participants think should change and "where," to increase its amount and quality. To illuminate "how" things might change, the same data is then re-analysed deductively against six 'lessons learnt' from a 2012 review of literature examining the diffusion of innovative teaching and learning in higher education. Lessons are confirmed or lacunae pointed out, before the concluding discussion offers recommendations and observations for universities pursuing research-rich education.