The proposed optimization method of test accesses, with a combined BIST and external test (CBET) scheme, can minimize the test time and eliminate the wasteful usage of external pins by considering the trade-off between test time and the number of external pins. Our idea consists of two parts. One is to determine the optimum groups, each of which consists of cores, to simultaneously share mechanisms for the external test. The other is to determine the optimum bandwidth of the external input and output for the external test. We design the external test part to be under the full bandwidth of external pins by considering the trade-off between the test time and the number of external pins. This is achieved only with the CBET scheme because it permits test sets for both the BIST and the external test to be elastic. Taking the test bus architecture as an example, a formulation for test access optimization and experimental results are shown. Experimental results reveal that our optimization can achieve a 51.9% reduction in the test time of conventional test scheduling and our proposals are confirmed to be effective in reducing the test time of system-on-a-chip.