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We use ab initio calculations to examine thermodynamic factors that could promote the formation of recently proposed unique oP10-FeB₄ and oP12-FeB₂ compounds. We demonstrate that these compact boron-rich phases are stabilized further under pressure. We also show that chromium tetraboride is more stable in the new oP10 rather than the reported oI10 structure which opens up the possibility of realizing an oP10-(Fe_xCr_1-x)B₄ pseudobinary material. In addition to exhibiting remarkable electronic features, oP10-FeB₄ and oP12-FeB₂ are expected to be harder than the known Fe–B compounds commonly used for hard coating applications.