Adaptive Comparative Judgement (ACJ) is a modification of Thurstone's method of comparative judgement that exploits the power of adaptivity, but in scoring rather than testing. Professional judgement by teachers replaces the marking of tests; a judge is asked to compare the work of two students and simply to decide which of them is the better. From many such comparisons a measurement scale is created showing the relative quality of students' work; this can then be referenced in familiar ways to generate test results. The judges are asked only to make a "valid" decision about quality, yet ACJ achieves extremely high levels of "reliability," often considerably higher than practicable operational marking can achieve. It therefore offers a radical alternative to the pursuit of reliability through detailed marking schemes. ACJ is clearly appropriate for performances like writing or art, and for complex portfolios or reports, but may be useful in other contexts too. ACJ offers a new way to involve all teachers in summative as well as formative assessment. The model provides strong statistical control to ensure quality assessment for individual students. This paper describes the theoretical basis of ACJ, and illustrates it with outcomes from some of our trials. (Contains 3 figures and 2 tables.)