The critical current density, jc, of high-pressure synthesized MgB2-based balk materials correlates with the amount and distribution of higher borides (MgB12) and Mg-B-O inclusions, which in tern correlates with the synthesis temperature and presence of additions (Ti, Ta, SiC). High-pressure-synthesized materials with near MgB12 composition of matrix exhibited superconducting transition temperature, Tc, of about 37 K, rather high jc (5∙105 and 103 A/cm2 in 0 T and 3.5 T, respectively, at 20 K) and doubled matrix microhardness: 25±1.1 GPa at 4.9 N –load as compared to materials with MgB2).