Formal concept analysis (FCA) is increasingly applied to data mining problems, essentially as a formal framework for mining reduced representations (bases) of target pattern families. Yet most of the FCA-based miners, closed pattern miners, would only extract the patterns themselves out of a dataset, whereas the generality order among patterns would be required for many bases. As a contribution to the topic of the (precedence) order computation on top of the set of closed patterns, we present a novel method that borrows its overall incremental approach from two algorithms in the literature. The claimed innovation consists of splitting the update of the precedence links into a large number of lower-cover list computations (as opposed to a single uppercover list computation) that unfold simultaneously. The resulting method shows a good improvement with respect to its counterpart both on its theoretical complexity and on its practical performance. It is therefore a good starting point for the design of efficient and scalable precedence miners.