Models of non-common priors—in which agents “agree to disagree”—have been used to explain the sort of speculative trade observed in financial markets, which is widely recognized as inconsistent with traditional common-priors models. While non-common-priors models can elegantly explain such trade, we further explore the relationship between the distribution of information among traders and the trades that would be generated by these models in contractually rich zero-sum settings. We establish a series of results showing that trade flows in the direction of disagreements and not private information. For instance, non-common-priors models predict that private information often impedes trade in the same way that it does in common-priors models, and that market participants will not typically trade in the direction of their private information. We note that failures to account for others’ information may better explain these trading patterns.