Higher critical current densities, jc, (up to 1.6–0.15MA/cm2 at 10–35K) at low magnetic fields can be attained in MgB2-based materials, if a high manufacturing temperature (1050°C) is used, while low temperatures (600–800°C) usually lead to higher critical currents in high magnetic fields (10–4kA/cm2 in 6–10T at 10K). This tendency was observed for MgB2-based materials having 55–99% density and 17–98% connectivity, which were prepared by different methods from different precursors in a wide range of pressure (0.1MPa–2GPa). The variation of the manufacturing temperature led to a redistribution of the magnesium, boron, and impurity oxygen. At 2GPa, its increase results in the segregation of the oxygen in MgB2 and the transformation of 15–20nm thick layers of MgB0.6–0.8O0.8–0.9 into separate MgB0.9–3.5O1.6–2 grains and to a reduction of the size of MgB11–13O0.2–0.3 inclusions located in the MgB2 (MgB2.2–1.7O0.4–0.6) matrix. The size reduction of B-enriched inclusions and the localization of O in MgB2 seem to be the reason for the increase of jc in low fields and for the shift from grain boundary to point pinning of vortices witnessed by an increase of the k-ratio.