Question generation from knowledge bases (or knowledge base question generation, KBQG) is the task of generating questions from structured database information, typically in the form of triples representing facts. To handle rare entities and generalize to unseen properties, previous work on KBQG resorted to extensive, often ad-hoc pre-and post-processing of the input triple. We revisit KBQG-using pre-training, a new (triple, question) dataset and taking question type into account-and show that our approach outperforms previous work both in a standard and in a zero-shot setting. We also show that the extended KBQG dataset (also helpful for knowledge base question answering) we provide allows not only for better coverage in terms of knowledge base (KB) properties but also for increased output variability in that it permits the generation of multiple questions from the same KB triple. Our code and dataset can be found at: https://gitlab.inria.fr/hankelvin/wikidataqg