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The restoration-based compaction procedures are the most computationally efficient static compaction procedures that reduce the length of a test sequence for a synchronous sequential circuit without reducing the fault coverage. We study one of the important components of the restoration-based compaction process, the initial omission process. This process selects test vectors that will be omitted from the test sequence initially, to start the restoration process. We also propose a specific procedure for the initial omission process. Experimental results for a variety of circuits and test sequences demonstrate that this procedure has a significant effect on the compacted test sequence length. Intuitively, the new procedure postpones the point at which the compaction procedure saturates, thus allowing smaller test lengths to be obtained before saturation is reached. The importance of continuing to explore this problem is related to the fact that static compaction procedures for synchronous sequential circuits are important for scan circuits as well.