Background: Normalization is essential to ensure accurate analysis and proper interpretation of sequencing data, and chromosome conformation capture data such as Hi-C have particular challenges. Although several methods have been proposed, the most widely used type of normalization of Hi-C data usually casts estimation of unwanted effects as a matrix balancing problem, relying on the assumption that all genomic regions interact equally with each other. Results: In order to explore the effect of copy-number variations on Hi-C data normalization, we first propose a simulation model that predict the effects of large copy-number changes on a diploid Hi-C contact map. We then show that the standard approaches relying on equal visibility fail to correct for unwanted effects in the presence of copy-number variations. We thus propose a simple extension to matrix balancing methods that model these effects. Our approach can either retain the copy-number variation effects (LOIC) or remove them (CAIC). We show that this leads to better downstream analysis of the three-dimensional organization of rearranged genomes. Conclusions: Taken together, our results highlight the importance of using dedicated methods for the analysis of Hi-C cancer data. Both CAIC and LOIC methods perform well on simulated and real Hi-C data sets, each fulfilling different needs.