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Extending previous work on monotonicity in morphology and morphosyntax, I argue that some of the most important constraints in syntax can be analyzed in terms of monotonic functions that map specific kinds of syntactic representations to fixed, universal hierarchies. I cover the Ban Against Improper Movement, the Williams Cycle, the Ban Against Improper Case, and omnivorous number. The general method of analysis is remarkably similar across all phenomena, which suggests that monotonicity provides a unified perspective on a wide range of phenomena in syntax as well as morphology and morphosyntax. I also argue that syntax, thanks to extensive work in computational syntax, provides a unique opportunity to probe whether the prevalence of monotonicity principles in natural language is due to computational complexity considerations. Not only, then, is it possible to extend the purview of monotonicity from semantics to syntax, doing so might yield new insights into monotonicity that would not be obtainable otherwise.