If T is any finite higher commutator in an associative ring R, for example, T = [[R, R], [R, R]], and if T has minimal cardinality so that the ideal generated by T is infinite, then T is in the centre of R and T 2 = 0. Also, if T is any finite, higher commutator containing no nonzero nilpotent element then T generates a finite ideal.2010 Mathematics subject classification: primary 16W10; secondary 16R50, 16D25.