A major argument for process-based approaches to nonconcatenative morphology is the observation that mutation morphology (morphological categories expressed by changes in tone, stress, segmental quality or quantity) seem to exhibit a systematic asymmetry: Affixal morphology cyclically triggers changes in the bases to which it attaches, but bases don’t trigger comparable ‘anticyclic’ changes in affixes (Inkelas 1998, Alderete 2001, Rolle 2018). Intuitively, processes (morphology) can affect objects (stems), but objects cannot affect processes. Alderete (2001) calls this generalization ‘Strict Base Mutation’. Inkelas (1998) argues that it follows from approaches where mutation is the effect of morphophonological constraints but is unexpected in item-and-arrangement models where mutation is the effect of defective floating material (Lieber 1992, Wolf 2007, Bye & Svenonius 2012), in the terms of Bermúdez-Otero (2012) ‘Generalized Nonlinear Affixation’. This paper has three goals: First, we provide extensive typological evidence that Strict Base Mutation is empirically wrong presupposing a standard lexicalist cophonology approach: Anticyclic mutation exists for all major phonological modalities. Second, we demonstrate that the attested types of anticyclic mutation directly follow from a standard Generalized Nonlinear Affixation approach to cyclic mutation couched in the formal framework of Colored Containment Theory (van Oostendorp 2008, Trommer 2011, Zimmermann 2017). Third, we show that recent reformulations of the SBM in non-lexicalist models such as Cophonologies by Phase (Sande et al. 2020), and the model developed in Rolle (2018), while solving some of the problems raised by the Strict Base Mutation hypothesis in standard cophonology theory, still make problematic empirical predictions.