The 'pollen test' and 'fruit set test' following controlled crossing combinations of parents are the most commonly used methods for pollination incompatibility studies in Olea europaea L. Self-incompatibility (SI), with diagnoses based on the pollen test and pollen germination, indicating self-compatibility, is not always followed by fruit set in this species. To solve this dispute, we have reconciled all observations into a new model. Mismatches between field and laboratory data and between methods are resolved by the dual-successive-screen model (DSSM) supposing two different loci for the expression of the two SI mechanisms. Pollen/stigma is controlled by diallelic SI, or DSI, inferring two G1 and G2 compatibility/incompatibility (C/I) groups for varieties, whereas pollen tubes in ovaries are controlled by poly-allelic SI or PASI with twenty C/I groups. To explain the selfing of varieties, we have suggested that some determinants in the pollen tube and stigma are unstable and degrade (DS-D for degradation of S-determinant) after three to five days, enabling some pollen tubes to avoid being rejected, hence reaching ovules. DSI and PASI in the DSSM and DS-D mechanisms, plus the andromonoecy of the olive tree, complexify SI studies. Inferences from DSSM and DS-D mechanisms in olive orchard practice are detailed.