We study pseudo-Anosov mapping classes with bounded normalized Weil-Petersson translation distance (and unbounded genus). In analogy with a result of Farb-Leininger-Margalit for Teichmuller translation distances, we show all such mapping classes fit together into a finite collection of cusped hyperbolic 3-manifolds, where the cusps are filled to become either vertical (transverse to fibers) or horizontal (parallel to fibers). This is joint work with Chris Leininger, Juan Souto and Sam Taylor.