We show how the so-called distributional characteristic of a policy instrument can be additively decomposed into two components: one that captures the targeting efficiency of the instrument, the other its redistributive efficiency. Using these measures, we provide an interpretation of the commonly used leakage and undercoverage rates (and other indices based on these concepts) within standard welfare theory. Essentially, one can interpret such indices as special (and restrictive) cases of the targeting efficiency index. As well as failing to capture the relative redistributive efficiencies of policy instruments, they also implicitly assume a set of value judgments consistent only with the commonly used poverty gap. For illustrative purposes, we present an empirical application of the decomposition approach to Mexican data.