Copy number alterations (CNAs) in cancer patients show a large variability in their number, length and position, but the sources of this variability are not known. CNA number and length are linked to patient survival, suggesting clinical relevance. We have identified genes that tend to be mutated in samples that have few or many CNAs, which we term CONIM genes (COpy Number Instability Modulators). CONIM proteins cluster into a densely connected subnetwork of physical interactions and many of them are epigenetic modifiers. Therefore, we investigated how the epigenome of the tissue-of-origin influences the position of CNA breakpoints and the properties of the resulting CNAs. We found that the presence of heterochromatin in the tissue-of- origin contributes to the recurrence and length of CNAs in the respective cancer type.