The sky-blue emitting phosphorescent compound Ir(4,6-dFppy)(2)(acac) (FIracac) doped into different matrices is studied under ambient conditions and at cryogenic temperatures on the basis of broadband and high-resolution emission spectra. The emitting triplet state is found to be largely of metal-to-ligand charge transfer (MLCT) character. It is observed that different polycrystalline and amorphous hosts distinctly affect the properties of the triplet. Moreover, a comparison of FIracac with the related Ir(4,6-dFppy)(2)(pic) (FIrpic), differing only by the ancillary ligand, reveals obvious changes of properties of the emitting state. These observations are explained by different effects of acac and pic on the Ir(III) d-orbitals. In particular, the occupied frontier orbitals, strongly involving the t(2g)-manifold, and their splitting patterns are modified differently. This influences spin-orbit coupling (SOC) of the emitting triplet state to higher-lying 1,3(MLCT) states. As a consequence, zero-field splittings, radiative decay rates, and phosphorescence quantum yields are changed. The important effects of SOC are discussed qualitatively and are related to the emission properties of the individual triplet substates, as determined from highly resolved spectra. The results allow us to gain a better understanding of the impact of SOC on the emission properties with the aim to develop more efficient triplet emitters for OLEDs.