Reduction in compensation in Si-doped Al-rich AlGaN is demonstrated via chemical potential control (CPC). The chemical potentials and the resulting formation energies of carbon on the nitrogen site (CN) and cation vacancy complex with Si (VIII + nSiIII) were related to growth variables through a thermodynamic supersaturation model, which quantitatively predicted the incorporation of CN and the generation of the VIII + nSiIII complex. The compensation "knee" behavior, i.e., decreasing conductivity with increasing Si incorporation beyond a certain concentration, was successfully controlled. The maximum free carrier concentration was improved by impeding the formation of VIII + nSiIII complexes under III-richer conditions, while the impurity compensation by CN was reduced by making the growth environment N-richer. The results of Hall effect measurement and photoluminescence agreed well with quantitative theoretical predictions of the CPC model. Based on the developed model, the highest conductivity of 160 Ω-1 cm-1 with free carrier concentration of 3 × 1019 cm-3 in Al0.7Ga0.3N ever reported was achieved on single crystal AlN substrates. The demonstrated predictive power of the CPC model should greatly reduce the empirical analysis or iterative experimentation that would otherwise be necessary.