We introduce a notion of complexity for interpretations, which is used to prove some new results about interpretations of sequential theories. In particular, we give a new, elementary proof of Pudlak's theorem that sequential theories are connected. We also demonstrate a counterexample to the infinitary distributive law $a \vee \bigwedge_{i \in I} b_i = \bigwedge_{i \in I} (a \vee b_i)$ in the lattice of chapters, in which the chapters $a$ and $b_i$ are compact. (Counterexamples in which $a$ is not compact have been found previously.)