  We classify simple flops on smooth threefolds, or equivalently, Gorenstein
threefold singularities with irreducible small resolution. There are only six
families of such singularities, distinguished by Koll{\'a}r's {\em length}
invariant. The method is to apply invariant theory to Pinkham's construction of
small resolutions. As a by-product, generators of the ring of invariants are
given for the standard action of the Weyl group of each of the irreducible root
systems.
