Sequential test generators fail to yield tests for some stuck-at-faults because they are unable to reach certain states necessary for exciting/propagating these target faults. Adding scan to the circuit increases reachability of these hard- to-reach and/or previously unreachable states. In this paper, we postulated that fewer scan ip- ops are needed to make these states reachable. The states necessary for detecting the hard-to-detect faults, when reached, will facilitate reaching other hard-to-reach states in one or more hops by the sequential test generator, resulting in significantly higher fault coverage. We collect information on the hard-to-reach, aborted, and easy states in our analysis. Results from our approach have indicated that higher fault coverage can be achieved with significantly fewer scan ip- ops for some circuits.