To ensure equal replication of the genome in every eukaryotic cell cycle, replication origins fire only once each S phase and do not fire after passive replication. Failure in these controls can lead to local amplification, contributing to genome instability and the development of cancer. To identify features of replication origins important for such amplification, we have investigated origin firing and local genome amplification in the presence of excess helicase loaders Cdc18 and Cdt1 in fission yeast. We find that S phase controls are attenuated and coordination of origin firing is lost, resulting in local amplification. Specific origins are necessary for amplification but act only within a permissive chromosomal context. Origins associated with amplification are highly AT-rich, fire efficiently and early during mitotic S phase, and are located in large intergenic regions. We propose that these features predispose replication origins to re-fire within a single S phase, or to remain active after passive replication.