The effective construction of many association rule bases requires the computation of both frequent closed and frequent generator itemsets (FCIs/FGs). However, these two tasks are rarely combined. Most of the existing solutions apply levelwise breadth-first traversal, though depth-first traversal, depending on data characteristics, is often superior. Hence, we address here a hybrid algorithm that combines the two different traversals. The proposed algorithm, Eclat-Z, extracts frequent itemsets (FIs) in a depth-first way. Then, the algorithm filters FCIs and FGs among FIs in a levelwise manner, and associates the generators to their closures. In Eclat-Z we present a generic technique for extending an arbitrary FI-miner algorithm in order to support the generation of minimal non-redundant association rules too. Experimental results indicate that Eclat-Z outperforms pure levelwise methods in most cases.