We have investigated the influence of composition gradients on the microdomain structure and viscoelastic properties of tapered block copolymers by (i) varying the amount of interfacial material and (ii) the block sequence. Normal tapered and inverse tapered triblock copolymers of polystyrene and polyisoperne with a tapered midblock have been synthesized via anionic polymerization with a nearly symmetric composition and compared with the corresponding diblock copolymers. We found that increasing the amount of tapered material within the interface systematically increases the compatibility. Block sequencing is found to be an important factor controlling compatibility. Inverse tapered block copolymers are much more compatible than the corresponding normal tapered block copolymers. Results presented here could be used as a guideline for preparing copolymers with controlled compatibility at the synthesis level.