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We introduce two criteria to regularize the optimization involved in learning a classifier in a domain where no annotated data are available, leveraging annotated data in a different domain, a problem known as unsupervised domain adaptation. We focus on the task of semantic segmentation, where annotated synthetic data are aplenty, but annotating real data is laborious. The first criterion, inspired by visual psychophysics, is that the map between the two image domains be phase-preserving. This restricts the set of possible learned maps, while enabling enough flexibility to transfer semantic information. The second criterion aims to leverage ecological statistics, or regularities in the scene which are manifest in any image of it, regardless of the characteristics of the illuminant or the imaging sensor. It is implemented using a deep neural network that scores the likelihood of each possible segmentation given a single un-annotated image. Incorporating these two priors in a standard domain adaptation framework improves performance across the board in the most common unsupervised domain adaptation benchmarks for semantic segmentation.