Structural (manual or automated) testing today often overlooks typical programming faults because of inherent flaws in the simple criteria applied (e.g. branch or all-uses). Dedicated testing strategies that address such faults (e.g. mutation testing) are not specifically designed for smart automatic test case generation. In this paper we present a new coverage criterion and its implementation that accomplishes both: it detects more faults and integrates easily into automated test case generation. The criterion is targeted towards unveiling faults that originate from shifts in the equivalence classes that are caused by small coding errors (inspired by mutation testing). On benchmark codes from the Java-API and from an open-source project we improve the fault detection capability by up to 41\% compared to branch and all-use coverage.