|Abstract:||Complex segments - segments with multiple, unordered place features - are most common in African languages. Understanding the phonology of clicks and labial-velars is a crucial step in understanding the phonology of African languages. This paper examines both these types of complex segments from the point of view of simplification, a special instance of segmental reduction. This is a type of process where a complex stop is realized on the surface as a simple stop, and it is related to neutralization processes in general. Empirically, labial- velars are found to reduce to either simple labials or simple dorsals. Clicks reduce to simple dorsals. The theory is based in OT and accounts for these simplification processes using general and independently-motivated constraints and place markedness hierarchies. All attested patterns of simplification are predicted, and constraints controlling for complexity within a language are derived from this universal hierarchy. This computational system allows for segmental representations to be simplified, without reference to an abstract, primary place.