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Description: A foundational goal of linguistics is to investigate whether shared features of the human cognitive system can explain how linguistic patterns are distributed across languages. In this study we report a series of artificial language learning experiments to test a hypothesised link between cognition and a persistent regularity of morpheme order: number morphemes (e.g., plural markers) tend to be ordered closer to noun stems than case morphemes (e.g., accusative markers) (Greenberg, 1963). We argue that this typological tendency may be driven by a bias favouring orders that reflect scopal relationships in morphosyntactic composition (Bybee, 1985; Rice, 2000; Culbertson & Adger, 2014). We taught participants an artificial language with noun stems, and case and number morphemes. Crucially, the input language indicated only that each morpheme preceded or followed the noun stem. Examples in which two (overt) morphemes co-occurred were held out—i.e., no instances of plural accusatives. At test, participants were asked to produce utterances, including the held-out examples. As predicted, learners consistently produced number closer to the noun stem than case. We replicate this effect with free and bound morphemes, pre- or post-nominal placement, and with English and Japanese speakers. However, we also find that this tendency can be reversed when the form of the case marker is conditioned on the noun, suggesting an influence of dependency length. Our results provide evidence that universal features of cognition may play a causal role in shaping the relative order of morphemes.