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This paper addresses the testability problems raised by intellectual property cores with multiple clock domains. The proposed solution is based on a novel core wrapper architecture and a new wrapper design algorithm. It is shown how multifrequency at-speed test response capture can be achieved via the design of capture windows without any structural modifications to the logic within the embedded core. The new features in the core wrapper architecture, which introduce limited hardware overhead, can also synchronize the external tester channels with the core's internal scan chains in the shift mode. Thus, the wrapper implementation space can be explored in order to efficiently utilize the available tester bandwidth while meeting the constraints on the maximum internal shift frequency that guarantees low testing time within the given power ratings. Using experimental data, the benefits of the proposed solution are demonstrated by analyzing the tradeoffs between the number of tester channels, testing time, area overhead, and power dissipation.