The critical current density, Jc, of single crystals of Ba2YCu3O7 is comparable to that of melt-textured-growth materials as well as to the intragrain Jc of bulk polycrystalline Ba2YCu3O7. Typical values at 77 K and 9 kOe are near 5x 103 A/cm2, and are presumably limited by weak pinning. We have obtained a significant enhancement of this pinning-limited Jc by three techniques: 1) a short reannealing procedure, 2) fast neutron irradiation, and 3) proton irradiation. Interestingly, the combination of the first technique followed by either irradiation is not as effective as the iradiation alone. That is, the best candidates for irradiation are not necessarily those with the highest initial Jc.