Styrene–isoprene block copolymers with a different degree of monomer distribution are hydrogenated with homogeneous catalysts. The products are characterized by means of IR and 1H-NMR spectroscopy, GPC, viscometry, and light scattering. Hydrogenation proceeds without destruction and selectively for olefinic unsaturation. The hydrogenated copolymers are homogeneous in molecular weights and chain composition. The influence of the copolymer structure on the solution properties in selective solvents is established. In cyclohexane an equilibrium between micelle associates and individual polymer coils, monomolecular micelles, or micelle aggregates are observed, depending on the type of the copolymer. The micellization in base-lubricating oil leads to micelle fractions with a different degree of association.