A method and apparatus for providing ordered capture clocks to detect or locate faults within N clock domains and faults crossing any two clock domains in a scan-based integrated circuit or circuit assembly in self-test or scan-test mode, where N>1 and each domain has a plurality of scan cells. The method and apparatus will apply an ordered sequence of capture clocks to all scan cells within N clock domains where one or more capture clocks must contain one or more shift clock pulses during the capture operation. A computer-aided design (CAD) method is further developed to realize the method and synthesize the apparatus. In order to further improve the circuit's fault coverage, a CAD method and apparatus are further developed to minimize the memory usage and generate scan patterns for full-scan and feed-forward partial-scan designs containing transparent storage cells, asynchronous set/reset signals, tri-state busses, and low-power gated clocks.