Steve White - University of California, Irvine (UCI) We have recently completed a study of the t-t'-J model on 8 and 6 leg cylinders. These results seem to apply qualitatively to the 2D system. We find that the t-t'-J model captures some of the physics of the cuprates well, but superconductivity itself is different in the model and the materials. I will report on our findings for the phase diagram of the model, including a novel "unpaired" striped phase and the coexistence of d-wave pairing, antiferromagnetic order, and p-wave triplet pairing.