This paper analyzes a type of rule-ordering paradox known as counterfeeding from the past (CFFTP), which violates the transitivity condition on rule ordering. I assume a substance-free version of rule-based phonology, which predicts such paradoxes to be impossible. This distinguishes my theory from several versions of Optimality Theory, which have been shown to generate CFFTP. I evaluate this predictive difference between theories using a typological survey of CFFTP, concluding that contrary to what has been claimed in the literature, there are no convincing cases of this ordering paradox. In all languages, the argument for CFFTP is not justified by the data, or else the data can be reanalyzed without paradoxes in a transitivity-respecting grammar. While other theories overgenerate, rule-based phonology is thus restrictive enough to capture the typological data with respect to CFFTP. Additional time is spent on a variety of Arabic, where the resolution to the apparent paradox has interesting implications for the representation of prosody. I show that data which are conventionally analyzed in terms of syllable structure must be given a purely segmental analysis. This is in line with recent work moving towards flat representations of prosodic structure.