In Escherichia coli, like all organisms, DNA replication is coordinated with cell cycle progression to ensure duplication of the genome prior to cell division. Chromosome replication is initiated from the replication origin, oriC, by the DnaA protein associated with ATP. Initiations take place once per cell cycle and in synchrony at all cellular origins. DnaA also binds ADP with similar affinity as ATP and in wild-type cells the majority of DnaA molecules are ADP bound. In cells where the DnaA^ATP/DnaA^ADP ratio increases or in cells where DnaA^ATP has increased access to oriC, premature initiations take place, often referred to as overinitiation. Overinitiating cells are generally characterized by their slow growth and in the most severe cases lethal accumulation of DNA strand breaks. Here, we review the different strategies adopted by E. coli to survive overinitiation. We propose a unifying model where all mutations that suppress overinitiation keep replication forks separated in time and, thereby, reduce the formation of strand breaks. One group of mutations does so by lowering the activity of oriC and/or DnaA to reduce the frequency of initiations to an acceptable level. In the other group of mutations, replication forks are kept apart by preventing formation of damages that would otherwise cause replication blocks, by allowing bypass of replication blocks and/or by slowing down replication forks. This group of suppressors restores viability despite excessive chromosome replication and provides new insights into mechanisms that safeguard DNA integrity.