Measurements of the electrical resistivity, ρ, and of the critical current, I c , of polycrystalline Y 1 Ba 2 Cu 3 O 7 - δ samples before and after being melted superficially are presented. The melting was done by heating the samples at 1050°C during a few minutes, and then annealing at 900°C in flowing oxygen during several hours. This melting process may increase I c by up to two orders of magnitude, while ρ changes by a factor of three or less. Scanning electron microscopy (SEM) and optical microscopy with polarization of the cross-section of the sample suggests that in the melted surface a grain alignment (typically 50 μm to 100 μm deep), similar to that observed in the whole volume in textured samples, appears. We relate such an important increase of I c and the slight variations in ρ with differences of the spatial current density redistributions associated with these two quantities (in surface for I c and in volume for ρ).