The authors have fabricated bulk samples of high-Tc oxide superconductors with narrow inductive Tc transitions ( approximately 3 K) and low resistivities ( rho (100 K):250-1000 mu Omega cm). They find such samples to have improved transport critical current density (Jct) properties. Although Jct decreases rapidly with increasing field for fields <1 T, Jct is then approximately independent of field over the range 2-15 T at 4.2 K; at 77 K the field dependence is also much reduced. Jct is about the same whether the applied current is parallel to or perpendicular to the applied field. The high-field values of Jct are, however, still small (<or approximately=50 A cm-2), but are much higher than previous samples in which S-N-S tunnelling controlled Jct, reducing it to less than 1 A cm-2 in fields of approximately 1 mT at 77 K. DC magnetisation data demonstrate that the local critical current density within the individual grains is as high as 107 A cm-2 in fields up to 20 T at 4.2 K. The evidence that the low Jct is the result of easy flux shear along the grain boundaries, as well as that suggesting percolative processes operate, is discussed.