This paper offers a broad empirical morphosyntactic study contributing to three debates in linguistics, one of long standing (the so-called equi-complexity axiom), the other two rather more recent, namely McWhorter’s claim (2001 a, b, 2007) that (pidgins and) creoles have the simplest grammars, and Trudgill’s claim (2009) that high-contact varieties of English are characterized by structural simplification processes while low-contact varieties are the result of complexification processes. The paper will present the results of comparative analyses covering three notionally different morphosyntactic complexity metrics applied to two different data types for about 50 largely non-standard varieties of English (low-contact L1s, high-contact L1s, L2s, pidgins and creoles). Ultimately, the study believes to be in a firm position to reject the axiom that the morphosyntax of all languages (and varieties of a language) is equally complex and to support both the claims by McWhorter and Trudgill.