The issue of 'predatory publishing', and indeed unscholarly publishing practices, affects all academics and li-brarians around the globe. However, there are some flaws in arguments and analyses made in several papers published on this topic, in particular those that have relied heavily on the blacklists that were established by Jeffrey Beall. While Beall advanced the discussion on 'predatory publishing', relying entirely on his blacklists to assess a journal for publishing a paper is problematic. This is because several of the criteria underlying those blacklists were insufficiently specific, excessively broad, arbitrary with no scientific validation, or incorrect identifiers of predatory behavior. The validity of those criteria has been deconstructed in more detail in this paper. From a total of 55 criteria in Beall's last/latest 2015 set of criteria, we suggest maintaining nine, elimi-nating 24, and correcting the remaining 22. While recognizing that this exercise involves a measure of subjec-tivity, it needs to advance in order to arrive - in a future exercise - at a more sensitive set of criteria. Fortified criteria alone, or the use of blacklists and whitelists, cannot combat 'predatory publishing', and an overhaul of rewards-based academic publishing is needed, supported by a set of reliable criteria-based guidance system.