A variant of the h-index introduced in García-Pérez (2009), called the iterated h-index, is studied to evaluate the productivity of scholars. It consists of successive applications of the h-index so as to obtain a vector of h-indices. In particular, the iterated h-index fixes a drawback of the h-index since it allows for (lexicographic) comparisons of scholars with the same h-index. Two types or results are presented. Firstly, we provide an axiomatic characterization of the iterated h-index, which rests on a new axiom of consistency and extensions of axioms in the literature to a richer framework. Secondly, we apply the h-index and iterated h-index to offer alternative sport rankings in tennis, football and basketball. These applications clearly demonstrate that the iterated h-index is much more appropriate than the classical h-index.