The incremental algorithm introduced in (Dale and Reiter, 1995) for producing distinguishing descriptions does not always generate a minimal description. In this paper, I show that when generalised to sets of individuals and disjunctive properties, this approach might generate unnecessarily long and ambiguous and/or epistemically redundant descriptions. I then present an alternative, constraint-based algorithm and show that it builds on existing related algorithms in that (i) it produces minimal descriptions for sets of individuals using positive, negative and disjunctive properties, (ii) it straightforwardly generalises to n-ary relations and (iii) it is integrated with surface realisation. .
