We have described the first successful application of a phosphite-oxazoline ligand library in the asymmetric Ir-catalyzed hydrogenation of several unfunctionalized olefins. The introduction of a bulky biaryl phosphite moiety in the ligand design is highly adventitious in the product outcome. By carefully selecting the ligand components, we obtained high activities (TOFs up to >1500 mol.(mol.h)(-1) at 1 bar of H-2) and enantioselectivities (ee values up to >99%) and, at the same time, show a broad scope for different substrate types. So, this is an exceptional ligand class that competes favorably with a few other ligand series that also provide high ee values for tri- and disubstituted substrate types.