In this paper we study a natural class of intersection numbers on
moduli spaces of degree d admissible covers from genus g curves to
P1, using techniques of localization. These intersection
numbers involve tautological λ and ψ classes, and are in
some sense analogous to Hodge Integrals on moduli spaces of stable curves.
We compute explicitly these numbers for all genera in degrees 2 and
3 and express the result in generating function form; we provide a
conjecture for the general degree d case.