From wafers where the AlOx barrier varies from junction to junction, we determine the proper oxidation conditions for spin-dependent tunnel junctions. We obtain large variation in the resistancexarea product (RxA) of the junctions within a wafer by either using nonuniform plasma oxidation on uniform Al films, or using uniform oxidation on Al films with a wedge thickness profile. When plotted against RxA, the tunneling magneto-resistance (TMR) for all junctions on the wafer falls on one curve that exhibits a broad maximum in the TMR. We propose that this maximum is where most metal Al has been oxidized while the oxidation of the bottom electrode is minimal. With annealing, we achieved our highest TMR, 38%, in highly resistive Co-AlOx-Co junctions. The most conductive junctions we made have about 18% TMR and RxA of 140 Omega mu m2. They are made by natural oxidation on about 5 Angstrom of Al. For barriers thinner than 13 Angstrom Al, we start to lose TMR for junctions larger than 2 mu m2. This is possibly caused by pinholes in thin barrier and indicates the importance of studying small size junctions. (C) 2000 American Institute of Physics. [S0021-8979(00)61608-0].