We theoretically study AlGaN/AlN/GaN heterostructures aimed at optimizing the AlGaN barrier for GaN-based high-electron-mobility transistors (HEMTs). Self-consistent Poisson–Schrödinger calculations combined with semi-empirical transport modeling are used to evaluate the two-dimensional electron gas (2DEG) concentration, sheet resistance, and saturation drain current as functions of barrier thickness and aluminum mole fraction. Technologically relevant constraints, including unintentional Ga incorporation, 2DEG-density-dependent mobility and saturation velocity, and the critical thickness of AlGaN coherently strained to GaN, are taken into account. Well-defined optimal barrier thicknesses minimize the sheet resistance to RS ~250 Ω/□, while the saturation drain current increases with barrier thickness and Al content, limited by strain-induced cracking. The results provide practical guidance for barrier design in GaN-based HEMTs.