Human languages enable robust generalization, letting us leverage our prior experience to communicate about novel meanings. This is partly due to language being compositional, where the meaning of a whole expression is a function of its parts. Natural languages also exhibit extensive variation, encoding meaning predictably enough to enable generalization without limiting speakers to one and only one way of expressing something. Previous work looking at the languages that emerge between neural networks in a communicative task has shown languages that enable robust communication and generalization reliably emerge. Despite this those languages score poorly on existing measures of compositionality leading to claims that a language's degree of compositionality has little bearing on how well it can generalise. We argue that the languages that emerge between networks are in fact straightforwardly compositional, but with a degree of natural language-like variation that can obscure their compositionality from existing measures. We introduce 4 measures of linguistic variation and show that early in training measures of variation correlate with generalization performance, but that this effect goes away over time as the languages that emerge become regular enough to generalize robustly. Like natural languages, emergent languages appear able to support a high degree of variation while retaining the generalizability we expect from compositionality. In an effort to decrease the variability of emergent languages we show how reducing a model's capacity results in greater regularity, in line with claims about factors shaping the emergence of regularity in human language.