Although often a painful and prolonged process, conjugating verbs correctly is essential when you try to master a foreign language. Verbs that exhibit an irregular conjugation paradigm, however, are often the verbs that occur most frequently in a language. The nature of inflectional morphemes and the mechanism for conjugating verbs have been the topic of debate for 25 years now. This has led to many different accounts of the problem, both in the field of descriptive linguistics as well as in a range of modeling approaches. The field of Construction Grammar has recently witnessed the theoretical work on Construction Morphology by Geert Booij (2010), but there has been no computational implementation that could test the theory on a large scale. Using the framework of Fluid Construction Grammar (FCG), I investigate the grammar and morphological constructions that are needed to automatically conjugate the full paradigms of the 600 most frequently used verbs in Spanish. This paper reports a fully operational rule-based implementation of such a grammar and goes into the details of the constructions that support it. The results also show that morphological constructions are exemplary constructions since they combine two (or more) units (a stem and a suffix(es)) into a single meaningful unit (a conjugated verb form) that can be picked up by other discourse elements. Extensions towards embedding the conjugation constructions into a bigger grammar or automatically learning new morphological constructions remain the focus of future work.