There is a long-standing debate about the principles and mechanisms that constrain the combinatorial properties of affixes, in particular of English suffixes. One group of scholars argues for the existence of lexical strata with strong restrictions holding between the different strata. This view is disputed by scholars who claim that it is selectional restrictions of individual suffixes that are responsible for the combinatorial properties of suffixes. Most recently, Hay (2000, 2002) has proposed a psycholinguistic model of morphological complexity, according to which an affix which can be easily parsed out in processing should not occur inside an affix which cannot. This model has been called ``complexity based ordering''. The general claim is that affixes can be approximately ordered along a hierarchy of complexity, with more separable affixes at one end, and less separable affixes at the other end. More separable affixes can attach outside less separable affixes, but not vice-versa. The goal of this paper is to test the predictions of complexity based ordering through an investigation of 15 English suffixes and their potential 210 two-suffix combinations. Using large data-bases such as the British National Corpus, the CELEX lexical database, the OED and the internet, we investigate whether the attested and non-attested combinations are best explained by complexity based ordering or by the individual selectional properties of these suffixes. We show that in most cases selectional restrictions and parsing restrictions coincide. Where selectional restrictions underdetermine possible combinations, complexity based ordering makes correct predictions. Only easily parsable combinations are possible combinations, and this range of possible combinations is then further curtailed by selectional restrictions. In sum, we argue that both selectional restrictions and parsing constraints are instrumental in determining possible and impossible suffix combinations.