A series of 4,1-polyisoprene-b-1,2-polybutadiene diblock copolymers of differing molecular weights and compositions were prepared by anionic polymerization. The polybutadiene blocks were selectively hydrogenated to poly(ethylethylene) using a homogeneous ruthenium catalyst. The double bonds in the polyisoprene blocks were subsequently modified to varying extents by the addition of difluorocarbene. The precursor polyisoprene-poly(ethylethylene) materials were disordered, but upon difluorocarbene (CF2) addition the effective degree of segregation in these materials increased markedly. Small-angle X-ray scattering was used to characterize the ordered state morphologies and domains spacings. Effective interaction parameters (χeff) were extracted from the temperature- and composition-dependent domain spacings, and these in turn were used to place the various samples on an experimental segregation vs composition phase map. The interaction parameter between poly(ethylethylene) and polyisoprene increases by a factor of 370 upon complete CF2 modification. This large enhancement enables examination of a much wider range of segregation strength than is accessible by varying temperature. A notable feature of these results is that the gyroid phase appears to be stable into the strong segregation regime, in contrast to expectations based on self-consistent-field theory.