Ex-situ Powder-In-Tube MgB2 tapes prepared with ball-milled, undoped powders showed a strong enhancement of the irreversibility field H*, the upper critical field Hc2 and the critical current density Jc(H) together with the suppression of the anisotropy of all of these quantities. Jc reached 104 A/cm2 at 4.2 K and 10 T, with an irreversibility field of about 14 T at 4.2 K, and Hc2 of 9 T at 25 K, high values for not-doped MgB2. The enhanced Jc and H* values are associated with significant grain refinement produced by milling of the MgB2 powder, which enhances grain boundary pinning, although at the same time also reducing the connectivity from about 12% to 8%. Although enhanced pinning and diminished connectivity are in opposition, the overall influence of ball milling on Jc is positive because the increased density of grains with a size comparable with the mean free path produces strong electron scattering that substantially increases Hc2, especially Hc2 perpendicular to the Mg and B planes.