We determine that exponential Welch permutations lead in general to the smallest maximal frequency hops among all Costas permutations, and are also relatively easy to study, as a closed formula exists for the maximal hop. Through extensive collection of data for logarithmic Welch and Golomb permutations, on the other hand, it is found that a) these 2 families behave (almost) identically, and that b) their maximal hops do not get as small as in exponential Welch permutations.