Systematic variation of comonomer concentration in individual polymer chains is responsible for unique phase behaviors in different types of copolymers. Controlled self-assembly of gradient copolymers into desired morphologies is theoretically understood but practically challenging, and identifying heterogeneous phase partitioning of individual comonomers in those resulting morphological regions can be difficult. Building on previous work where improved methods were used to elucidate heterogeneous comonomer partitioning in styrene butadiene gradient copolymers [Clough et al. Macromolecules 2014, 47, 2625], the arrangement of the styrene and butadiene monomers in only a fraction of the total chain length is used here to significantly perturb the overall morphology and physical properties of copolymers. Importantly, the chemical composition of all copolymers was held nearly fixed in this study. The resulting tapered and inverse tapered block copolymers contain nanometer length scale interfaces that differ from one another and differ dramatically from that observed in a control block copolymer composed of chains with a discrete interface. Evidence is presented that butadiene can reside in rigid environments, styrene can reside in mobile environments, and their relative amounts can be varied based on the gradient design. The connection between the molecular design of the gradient, the resulting nanometer-length scale interfacial structures, and mechanical properties is demonstrated using a combination of variable temperature solid-state NMR, modulated DSC (differential scanning calorimetry), AFM (atomic force microscopy), and rheology experiments.