It is often claimed that all grammars are equally complex. But more properly, it is increasingly agreed that all grammars are complex, but to varying degrees. In this talk I will demonstrate that when grammars are used at a point in their history more commonly as non-native languages than native ones, the result is a significant simplification of their grammatical structures, in terms of what will be described as OVERSPECIFICATION, STRUCURAL ELABORATION, and IRREGULARITY. Similar points have been made about creole languages (albeit just as often opposed). However, the observation also applies to standardized languages such as English, Persian, Mandarin Chinese, Standard Indonesian, and the colloquial Arabic varieties. Languages of this kind will be discussed, with proposals as to where they can be situated in a typology of language contact.