We report pulsed laser deposition being a quite suitable growth method for smooth and transparent p-type copper iodide (CuI) thin films with tailored electrical properties. The film characteristics are strongly influenced by the temperature during growth. Increasing substrate temperatures result in significant improvements in crystallinity compared to deposition at room temperature. In contrast to other growth techniques, the hole carrier density p can be varied systematically between 5 × 1016 cm−3 and 1 × 1019 cm−3 with hole mobilities up to 20 cm2/V s for lowest p. The surfaces exhibit irregularly shaped grains, and the roughness can be decreased down to 1 nm. Furthermore, the samples exhibit high transmittance up to 90% in the visible spectrum.