We investigate whether block copolymers of controlled effective segregation strength can be designed via a novel controlled radical polymerization technique that allows statistical polymerization of different monomers in either one of the constituting blocks: We examine the morphologies and segregation regimes of two families of poly(styrene-stat-(acrylic acid))-b-poly(acrylic acid) diblocks of different block ratios (i.e., one asymmetric and one symmetric), comprising a statistical first block of variable ratio of styrene vs acrylic acid and a second PAA block. Thanks to small-angle X-ray scattering and transmission electron microscopy, we observe that as the composition of the statistical first block is varied, such asymmetric and symmetric diblocks form strongly to weakly microphase-separated structures, respectively, presenting spherical and well-ordered lamellar symmetries, or homogeneous (disordered) phases. We thus demonstrate that the segregation strength can be quantitatively controlled by the composition of the statistical first block, regardless of the diblock symmetry.