The synthesis of tapered multiblock copolymers by statistical living anionic copolymerization of a mixture of isoprene (I) and 4-methylstyrene (4MS) in cyclohexane is based on vastly different reactivity ratios of I and 4MS (r(I) = 25.4 and r(4MS) = 0.007). A library of tapered multiblock copolymers was prepared with different molecular weights (approximate molecular weights of 80, 240, and 400 kg/mol) and number of blocks (P(I-co-4MS)(n) with 1 <= n <= 5), and their thermomechanical properties were investigated by differential scanning calorimetry, rheology, and tensile testing in relation to their nanodomain structure, the latter investigated by small-angle X-ray scattering. The interaction parameter between I and 4MS segments was obtained based on the order-to-disorder transition temperatures of a series of PI-b-P4MS diblock copolymers prepared by sequential addition of monomers. The obtained chi(T) dependencies (chi(MFT) = 23.2/T - 0.024 and chi(FH) = 36.0/T - 0.041) are weaker than in the corresponding PI-b-PS system, revealing that the different reactivity ratios of the monomers is not the sole factor that controls the miscibility of the segments in the tapered multiblock copolymers. The latter is controlled by the value of the interaction parameter, the width of the tapered interfaces, and the number of blocks and total molecular weight. Tapered multiblock copolymers undergo a fluctuation-induced first-order transition from the ordered to the disordered state. The domain spacing scales as d similar to n(-0.83 +/- 0.02) when compared under a fixed total molecular weight, reflecting the conformational properties of the middle blocks. In addition, the domain spacing depends on molecular weight, as d similar to N-0.55, revealing stretching of chains and nonideal configurations. These structural features of the tapered multiblock copolymer affected their mechanical properties. Tensile tests showed a dramatic enhancement of the strain at break with a concomitant increase in toughness. These mechanical properties can be fine-tuned by the judicious selection of molecular weight and number of blocks. The state of order (ordered, weakly ordered vs disordered) and proximity to the glass temperature of the hard phase are additional parameters that affect the mechanical response. The improved mechanical properties reflect the enhanced interfacial strength, the latter provided by the configurations of the middle blocks in the copolymers. The influence of methyl group substitution in the para position of styrene is discussed by comparing the self-assembly and thermomechanical properties of the current P(I-co-4MS)(n) with the P(I-co-PS)(n) system. We found that the shorter tapered interface in the former is counterbalanced by its lower effective interaction parameter resulting in similar domain spacings.