We report magnetic and electrical measurements of Nb Josephson junctions with strongly ferromagnetic barriers of Co, Ni, and Ni80Fe20 (Py). All these materials show multiple oscillations of critical current with a barrier thickness implying repeated 0-pi phase transitions in the superconducting order parameter. We show, in particular, that the Co barrier devices can be accurately modeled using existing clean limit theories and that, despite the high exchange energy (309 meV), the large IcR(N) value in the pi state means Co barriers are ideally suited to the practical development of superconducting pi-shift devices.