In the relational model, inclusion dependencies (INDs) convey many information on data semantics. They generalize foreign keys, which are very popular constraints in practice. However, one seldom knows the set of satisfied INDs in a database. The IND discovery problem in existing databases can be formulated as a data-mining problem. We underline in this article that the exploration of IND expressions from most general (smallest) INDs to most specific (largest) INDs does not succeed whenever large INDs have to be discovered. To cope with this problem, we introduce a new algorithm, called Zigzag , which combines the strength of levelwise algorithms (to find out some smallest INDs) with an optimistic criteria to jump more or less to largest INDs. Preliminary tests, on synthetic databases, are presented and commented on. It is worth noting that the main result of this paper is general enough to be applied to other data-mining problems, such as maximal frequent itemsets mining.