Systematic variation of the size and number of inverse-tapered blocks in styrene butadiene copolymers results in a wide range of accessible glass-transition temperatures (T-g), including T-g's approaching that predicted by the Fox equation. Composition-weighted average Tg's are expected for miscible blends or random copolymers, but such behavior has not previously been reported for block copolymers made from immiscible styrene and butadiene segments. In this work, 50:50 wt % multiblock copolymers with M-n = 120 000 kg/mol were synthesized using an inverse-tapered block design for all blocks except the end blocks. The total composition and molecular weight were held constant, but the type and number of blocks were systematically varied in order to compare contributions from the inverse-tapered chain interfaces to the overall glass transition behavior. Discrete copolymers of similar block number and length were investigated as controls to help separate contributions from the inverse-tapered design and the molecular weight of individual blocks. Some copolymers were intentionally designed such that individual block molecular weights were between the entanglement molecular weight (Me) of polystyrene (PS) and polybutadiene (PB). A range of intermediate glass transitions was observed, but the inverse-tapered copolymers that satisfied this latter condition were the only copolymers that exhibited a Tg near a composition-weighted average. Solid state NMR reveals dynamic heterogeneity among monomeric components through chain-level identification of relatively large amounts of rigid PB segments and mobile PS chain segments versus that observed in discrete block analogues where essentially all PB segments are mobile and all PS segments are rigid. NMR revealed subtle differences in the temperature-dependent segmental chain dynamics of different inverse-tapered blocks, which were not obvious from the calorimetric studies but which presumably contribute to the longer length scale Tg behavior.