Smaller universities may produce research which is on a par with larger, elite establishments. This is confirmed by a recently developed mathematical model, supported by data from British and French higher education research-evaluation exercises. The detailed nature of the UK system, in particular, allows quantification of the notion of critical mass in research. It is shown that research quality increases with group quantity, but only up to a limiting size referred to as the upper critical mass. The condition for smaller universities to produce top-quality research is that they contain research groups of sizes above the upper critical masses appropriate to their respective disciplines. Policies which concentrate support into progressively fewer, larger institutions are therefore unjustified for high-quality academic research. Instead, to amplify overall research strength, support for medium-sized groups should be prioritised to help them attain upper critical mass. (Contains 9 figures, 1 table and 2 notes.)