The frequent recurrence of copy number aberrations across tumour samples is a reliable hallmark of certain cancer driver genes. However, state-of-the-art algorithms for detecting recurrent aberrations fail to detect several known drivers. In this study, we propose RUBIC, an approach that detects recurrent copy number breaks, rather than recurrently amplified or deleted regions. This change of perspective allows for a simplified approach as recursive peak splitting procedures and repeated re-estimation of the background model are avoided. Furthermore, we control the false discovery rate on the level of called regions, rather than at the probe level, as in competing algorithms. We benchmark RUBIC against GISTIC2 (a state-of-the-art approach) and RAIG (a recently proposed approach) on simulated copy number data and on three SNP6 and NGS copy number data sets from TCGA. We show that RUBIC calls more focal recurrent regions and identifies a much larger fraction of known cancer genes.