The precision of an analysis based on abstract interpretation does not only depend on the abstract domain, but also on the solving method. The traditional solution is to solve iteratively abstract fixpoint equations, using extrapolation with a widening operator to make the iterations converge. Unfortunately, this extrapolation often loses crucial information for the analysis goal. A classical technique for improving the precision is ''widening with thresholds'', which bounds the extrapolation. Its benefit strongly depends on the choice of relevant thresholds. In this paper we propose a semantic-based technique for automatically inferring such thresholds, which applies to any control graph, be it intraprocedural, interprocedural or concurrent, without specific assumptions on the abstract domain. Despite its technical simplicity, our technique is able to infer the relevant thresholds in many practical cases.