Changes in gene dosage are a major driver of cancer, known to be caused by a finite, but increasingly well annotated, repertoire of mutational mechanisms. This can potentially generate correlated copy-number alterations across hundreds of linked genes, as exemplified by the 2% of childhood acute lymphoblastic leukaemia (ALL) with recurrent amplification of megabase regions of chromosome 21 (iAMP21). We used genomic, cytogenetic and transcriptional analysis, coupled with novel bioinformatic approaches, to reconstruct the evolution of iAMP21 ALL. Here we show that individuals born with the rare constitutional Robertsonian translocation between chromosomes 15 and 21, rob(15;21)(q10;q10)c, have approximately 2,700-fold increased risk of developing iAMP21 ALL compared to the general population. In such cases, amplification is initiated by a chromothripsis event involving both sister chromatids of the Robertsonian chromosome, a novel mechanism for cancer predisposition. In sporadic iAMP21, breakage-fusion-bridge cycles are typically the initiating event, often followed by chromothripsis. In both sporadic and rob(15;21)c-associated iAMP21, the final stages frequently involve duplications of the entire abnormal chromosome. The end-product is a derivative of chromosome 21 or the rob(15;21)c chromosome with gene dosage optimized for leukaemic potential, showing constrained copy-number levels over multiple linked genes. Thus, dicentric chromosomes may be an important precipitant of chromothripsis, as we show rob(15;21)c to be constitutionally dicentric and breakage-fusion-bridge cycles generate dicentric chromosomes somatically. Furthermore, our data illustrate that several cancer-specific mutational processes, applied sequentially, can coordinate to fashion copy-number profiles over large genomic scales, incrementally refining the fitness benefits of aggregated gene dosage changes. © 2014 Macmillan Publishers Limited.