We have investigated the influence of composition gradients on the microdomain structureand viscoelastic properties of tapered block copolymers by (i) varying the amount of interfacial materialand (ii) the block sequence. Normal tapered and inverse tapered triblock copolymers of polystyrene andpolyisoperne with a tapered midblock have been synthesized via anionic polymerization with a nearlysymmetric composition and compared with the corresponding diblock copolymers. We found that increasingthe amount of tapered material within the interface systematically increases the compatibility. Blocksequencing is found to be an important factor controlling compatibility. Inverse tapered block copolymersare much more compatible than the corresponding normal tapered block copolymers. Results presentedhere could be used as a guideline for preparing copolymers with controlled compatibility at the synthesislevel.