Analogies are 4-ary relations of the form "A is to B as C is to D". When A, B and C are fixed, we call analogical equation the problem of finding the correct D. A direct applicative domain is Natural Language Processing, in which it has been shown successful on word inflections, such as conjugation or declension. If most approaches rely on the axioms of proportional analogy to solve these equations, these axioms are known to have limitations, in particular in the nature of the considered flections. In this paper, we propose an alternative approach, based on the assumption that optimal word inflections are transformations of minimal complexity. We propose a rough estimation of complexity for word analogies and an algorithm to find the optimal transformations. We illustrate our method on a large-scale benchmark dataset and compare with state-of-the-art approaches to demonstrate the interest of using complexity to solve analogies on words.