The relationship between the entropy of language and its complexity has been the subject of much speculation – some seeing the increase of linguistic entropy as a sign of linguistic complexification or interpreting entropy drop as a marker of greater regularity. Some evolutionary explanations, like the learning bottleneck hypothesis, argues that communication systems having more regular structures tend to have evolutionary advantages over more complex structures. Other structural effects of communication networks, like globalization of exchanges or algorithmic mediation, have been hypothesized to have a regularization effect on language. Longer-term studies are now possible thanks to the arrival of large-scale diachronic corpora, like newspaper archives or digitized libraries. However, simple analyses of such datasets are prone to misinterpretations due to significant variations of corpus size over the years and the indirect effect this can have on various measures of language change and linguistic complexity. In particular, it is important not to misinterpret the arrival of new words as an increase in complexity as this variation is intrinsical, as is the variation of corpus size. This paper is an attempt to conduct an unbiased diachronic study of linguistic complexity over seven different languages using the Google Books corpus. The paper uses a simple entropy measure on a closed, but nevertheless large, subset of words, called kernels. The kernel contains only the words that are present without interruption for the whole length of the study. This excludes all the words that arrived or disappeared during the period. We argue that this method is robust towards variations of corpus size and permits to study change in complexity despite possible (and in the case of Google Books unknown) change in the composition of the corpus. Indeed, the evolution observed on the seven different languages shows rather different patterns that are not directly correlated with the evolution of the size of the respective corpora. The rest of the paper presents the methods followed, the results obtained and the next steps we envision.