We report on the phase state of two new diblock copolymer systems, poly(butadiene-b-tert-butyl methacrylate) (BBMA) and poly(ethylene-b-tert-butyl methacrylate) (EBMA). The EBMA system was synthesized from the BBMA by hydrogenation of the polybutadiene block, thus creating two systems at practically the same volume fractions and identical degrees of polymerization, but with different segment interaction parameters and conformational asymmetries. Hydrogenation of the butadiene block resulted in an increased incompatibility and to an asymmetric phase diagram. In one of the EBMA copolymers with a PE volume fraction f(PE) = 0.42, crystallization of the PE blocks was confined by the cylindrical mesophase in a fluid matrix. Upon PE crystallization, the hexagonal order was found to improve significantly following a matrix-assisted reorganization.