Transparent p-type materials with good mobility are needed to build completely transparent p-n junctions. Tin monoxide (SnO) is a promising candidate. A recent study indicates great enhancement of the hole mobility of SnO grown in Sn-rich environment [E. Fortunato et al., Appl. Phys. Lett. 97, 052105 (2010)]. Because such an environment makes the formation of defects very likely, we study defect effects on the electronic structure to explain the increased mobility. We find that Sn interstitials and O vacancies modify the valence band, inducing higher contributions of the delocalized Sn 5p orbitals as compared to the localized O 2p orbitals, thus increasing the mobility. This mechanism of valence band modification paves the way to a systematic improvement of transparent p-type semiconductors.