A semitoric integrable system $F=(J,H)$ on a symplectic $4$-manifold is simple if each fiber of $J$ contains at most one focus-focus critical point. Simple semitoric systems were classified about ten years ago by Pelayo-V~u Ngoc in terms of five invariants. In this paper we explain how the simplicity assumption can be removed from the classification by adapting the invariants.
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