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Copper(I) iodide, CuI, is the leading $p$-type non-toxic and earth-abundant semiconducting material for transparent electronics and thermoelectric generators. Defects play a crucial role in determining the carrier concentration, scattering process, and therefore thermoelectric performance of a material. A result of defect engineering, the power factor of thin film CuI was increased from $332\pm32$ {\mu}Wm$^{-1}$K$^{-2}$ to $578\pm58$ {\mu}Wm$^{-1}$K$^{-2}$ after implantation with noble gas ions (Ne, Ar, Xe). The increased power factor is due to a decoupling of the Seebeck coefficient and electrical conductivity identified through a changing scattering mechanism. Ion implantation causes the abundant production of Frenkel pairs, which were found to suppress compensating donors in CuI, and which scenario was also supported by density functional theory calculations. The compensating donor suppression led to a significantly improved Hall carrier concentration, increasing from $6.5\times10^{19}\pm0.1\times10^{19}$ cm$^{-3}$ to $11.5\times10^{19}\pm0.4\times10^{19}$ cm$^{-3}$. This work provides an important step forward in the development of CuI as a transparent conducting material for electronics and thermoelectric generators by introducing beneficial point defects with ion implantation., Comment: 7 pages, 4 figures, 57 references. The following article has been accepted by Applied Physics Letters. After it is published, it will be found at https://doi.org/10.1063/5.0233754