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System-on-chip (SOC) designs comprised of a number of embedded cores are widespread in today's integrated circuits. Embedded core-based design is likely to be equally popular for three-dimensional integrated circuits (3D ICs), the manufacture of which has become feasible in recent years. 3D integration offers a number of advantages over traditional 2D technologies, such as the reduction in the average interconnect length, higher performance, lower interconnect power consumption and smaller IC footprint. Despite recent advances in 3D fabrication and design methods, no attempt has been made thus far to design a 1500-style test wrapper for an embedded core that spans multiple layers in a 3D SOC. This study addresses wrapper optimisation in 3D ICs based on through-silicon vias (TSVs) for vertical interconnects. The authors objective is to minimise the scan-test time for a core under constraints on the total number of TSVs available for testing. The authors present an optimal solution based on an integer linear programming model as well as two polynomial-time heuristic solutions. Simulation results are presented for embedded cores from the ITC 2002 SOC test benchmarks.