Phonological constraints can, in principle, be classified according to whether they are natural (founded in principles of universal grammar (UG)) or unnatural (arbitrary, learned inductively from the language data). Recent work has used this distinction as the basis for arguments about the role of UG in learning. Some languages have phonological patterns that arguably reflect unnatural constraints. With experimental testing, one can assess whether such patterns are actually learned by native speakers. Becker, Ketrez, and Nevins (2007), testing speakers of Turkish, suggest that they do indeed go unlearned. They interpret this result with a strong UG position: humans are unable to learn data patterns not backed by UG principles. This article pursues the same research line, locating similarly unnatural data patterns in the vowel harmony system of Hungarian, such as the tendency (among certain stem types) for a final bilabial stop to favor front harmony. Our own test leads to the opposite conclusion of Becker and colleagues': Hungarians evidently do learn the unnatural patterns. To conclude we consider a bias account--that speakers are able to learn unnatural environments, but devalue them relative to natural ones. We outline a method for testing the strength of constraints as learned by speakers against the strength of the corresponding patterns in the lexicon, and show that it offers tentative support for the hypothesis that unnatural constraints are disfavored by language learners.