This paper describes a simple means to enable direct diagnosis by bypassing MISRs on a small set of tests (MISR-bypass test mode) while achieving ultimate output compression using MISRs for the majority of tests (MISR-enabled test mode.) By combining two compression schemes, XOR and MISRs in the same device, it becomes possible to have high compression and still support compression mode volume diagnostics. In our experiment, the MISR-bypass test was first executed and at 10% of the total test set the MISR-enabled test was performed. The results show that compared with MISR+XOR-based compression the proposed technique provides better volume diagnosis with slightly small (0.71 X to 0.97 X) compaction ratio. The scan cycles are about the same as the MISR-enabled mode. A possible application to partial good chips is also shown.