Abstract.We have fabricated two-dimensional arrays of superconducting quantum interference devices (SQUIDs) using YBa 2 Cu 3 O 7−δ ion-irradiated Josephson junctions and we have studied the effects of post annealing the arrays at 100• C in oxygen. The maximum voltage modulation, V B , in magnetic field for DC biased arrays at 50 K, initially is 1.2 mV but increases to 3 mV after annealing. Furthermore, the temperature where the largest VB occurs increases from 45 K to 48.5 K after annealing. We present and simulate a model where annealing causes diffusion and recombination of the low energy oxygen defects that narrows the barrier, resulting in an increase of the Josephson binding energy. We show that this process stabilizes after 40 minutes of annealing and leads to a significant improvement in the properties of the array.