This paper presents a novel reconfigurable powerconscious core test wrapper and discusses its application to optimal power-constrained SOC (system-on-chip) test scheduling. The advantage with the proposed wrapper is that at each core it allows (1) a exible TAM (test access mechanism) bandwidths, and (2) a possibility to select the appropriate test power consumption. Our scheduling technique, an extension of a preemptive scheduling approach,produces optimal solutions in respect to test time, and selects wrapper configurations in a systematic way that implicitly minimizes the TAM routing and the wrapper logic. Experimental results show the efficiency of our approach.