Testing embedded cores in a System-on-a-chip necessitates the use of a Test Access Mechanism, which provides for transportation of the test data between the chip and the core I/Os. To relax the requirements on the test access mechanism at the core output side, we outline a space and time compaction scheme which minimizes test application time and required test bandwidth at the same time. To implement a computationally feasible algorithm that searches for such an optimal compaction circuitry, we formulate the constraints, which avoid aliasing, on a mathematical basis. The experimental results illustrate that not only is performance optimized but furthermore the associated area overhead is low as well.