A library of readily available phosphite-oxazole/thiazole ligands (L1 a-g-L7 a-g) was applied in the Ir-catalyzed asymmetric hydrogenation of several largely unfunctionalized E- and Z-trisubstituted and 1,1-disubstituted terminal alkenes. The ability of the catalysts to transfer chiral information to the product could be tuned by choosing suitable ligand components (bridge length, the substituents in the heterocyclic ring and the alkyl backbone chain, the configuration of the ligand backbone, and the substituents/configurations in the biaryl phosphite moiety), so that enantioselectivities could be maximized for each substrate as required. Enantioselectivities were therefore excellent (enantiomeric excess (ee) values up to >99 %) for a wide range of E- and Z-trisubstituted and 1,1-disubstituted terminal alkenes. The biaryl phosphite moiety was a very advantageous ligand component in terms of substrate versatility.