AB diblock copolymers dissolved in a selective solvent for block B spontaneously self-assemble into spherical or cylindrical micelles with an A core surrounded by a corona of the B block. Using a Monte Carlo lattice model, we find that the sphere-to-cylinder transition can be fully described in terms of a packing parameter that depends on the relative cross sections of the two blocks. The latter can be Varied either by a block length being changed or by the B block being allowed to adopt an ordered conformation (e.g., helical). The model results are in good agreement with experimental observation. They also shed some light onto the molecular origins of the ease of processing and exceptional mechanical properties of spider dragline,