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In this work, we investigate the detection and estimation of multiple change-points in the mean of univariate data. A localised methodology is proposed for pruning down possibly conflicting change-point estimators computed from any change-point procedure that supplies the information about the local interval in which they are detected. We establish the theoretical consistency of the proposed localised pruning method in combination with the multiscale extension of the MOving SUM (MOSUM) procedure by Eichinger and Kirch (2018). Extensive simulation studies show the computational efficiency and good finite sample performance of the combined methodology.