I present a study on the morphological complexity of six European languages. A theory-free measure of the complexity of a language's inflectional morphology, is derived from Gell-Mann's concept of Effective Complexity. Using a parallel corpus, I show that disconsidering word order information results in the classical gradation of inflectional complexity: Languages in which words have more inflected variants seem to be more complex than languages with fewer variants. It also appears that the presence of the inflectional system increases the complexity of languages. However, when word order information is explicitly considered, the apparent gradation in complexity across languages vanishes. Furthermore, it becomes clear that the presence of inflections reduces the overall complexity of languages. In sum, inflection is used whenever its presence simplifies a language's description. Inflectional morphology is not a capricious feature, as some argue, but rather an effective tool for complexity reduction.