This paper presents a novel design-for-test (DFT) technique that allows core vendors to reduce the test complexity of a core they are trying to market. The idea is to design a core so that it can be tested with a very small number of test vectors. The I/O pins of such a "designed for high test compression" (DFHTC) core are identical to the I/O pins of an ordinary core. For the system integrator, testing a DFHTC core is identical to testing an ordinary core. The only difference is that the DFHTC core has a significantly smaller number of test vectors resulting in less test data as well as less test time (fewer scan vectors). This is achieved by carefully combining a parallel "test per clock" BIST scheme inside the core with the normal external testing scheme using a tester. The BIST structure inside the core generates weighted pseudo-random test vectors which detect a large number of faults in the core. Results indicate that such DFHTC cores have a significantly smaller number of test vectors than their ordinary counterparts thereby greatly reducing test time and test storage.