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Testing of three-dimensional (3D) stacked ICs (SICs) is starting to receive considerable attention in the semiconductor industry. Since the die-stacking steps of thinning, alignment, and bonding can introduce defects, there is a need to test multiple subsequent partial stacks during 3D assembly. We address the problem of test-architecture optimization for 3D stacked ICs to minimize overall test time when either the complete stack only, or the complete stack and multiple partial stacks, need to be tested. We show that optimal test-architecture solutions and test schedules for multiple test insertions are different from their counterparts for a single final stack test. In addition, we present optimization techniques for the testing of TSVs and die-external logic in combination with the dies in the stack.