To release micro-data tables containing sensitive data, generalization algorithms are usually required for satisfying given privacy properties, such as k-anonymity and l-diversity. It is well accepted that k-anonymity and l-diversity are proposed for different purposes, and the latter is a stronger property than the former. However, this paper uncovers an interesting relationship between these two properties when the generalization algorithms are publicly known. That is, preserving l-diversity in micro-data generalization can be done by preserving a new property, namely, l-cover, which is to satisfy l-anonymity in a special way. The practical impact of this discovery is that it may potentially lead to better heuristic generalization algorithms in terms of efficiency and data utility, that remain safe even when publicized.