When storage requirements or limits on test application time do not allow a complete (compact) test set to be used for a circuit, a partial test set that detects as many faults as possible is required. Motivated by this application, we address the following problem. Given a test sequence T of length L for a synchronous sequential circuit and a length MS of length at most M such that the fault coverage of TS is maximal. A similar problem was considered before for combinational and scan circuits and solved by test ordering. Test ordering is not possible with the single test sequence considered here for sequential circuits. We solve this problem by using a vector omission process that allows the length of the sequence T to be reduced while allowing minimal reductions in the number of detected faults. Using this process, it is possible to obtain a sequence TS that has the desired length and a maximal fault coverage.