The effect of doping with Ti, Ta, SiC in complex with synthesis temperature on the amount and distribution of structural inhomogeneities in MgB2 matrix of high-pressure-synthesized-materials (2 GPa) which can influence pinning: higher borides (MgB12) and oxygen-enriched Mg-B-O inclusions, was established and a mechanism of doping effect on jc increase different from the generally accepted was proposed. Near theoretically dense SiC-doped material exhibited jc= 106 A/cm 2 in 1T field and Hirr =8.5 T at 20 K. The highest jc in fields above 9, 6, and 4 T at 10, 20, and 25 K, respectively, was demonstrated by materials synthesized at 2 GPa, 600 °C from Mg and B without additions (at 20 K jc= 102 A/cm2 in 10 T field). Materials synthesized from Mg and B taken up to 1:20 ratio were superconductive. The highest jc (6×104 A/cm2 at 20 K in zero field, Hirr= 5 T) and the amount of SC phase (95.3% of shielding fraction), Tc being 37 K were demonstrated by materials having near MgB12 composition of the matrix. The materials with MgB12 matrix had a doubled microhardness of that with MgB2 matrix (251.1 GPa and 13.081.07 GPa, at a load of 4.9 N, respectively).