Escherichia coli DNA polymerase I exists in at least two distinct kinetic forms. When it binds to a template, the proofreading activity is usually switched off. As the enzyme progresses along the template, it becomes more and more competent for excision. This phenomenon introduces a link between fidelity and processivity. Processivity is best studied when the chain-length distributions of synthesized polymers are stationary. Even then, however, one cannot avoid multiple initiations on a given template by the same molecule of the enzyme. When synthesis is initiated with primers of lengths 15 or 20, a strange phenomenon is observed. It seems that the polymerase starts by hydrolyzing the primer down to a length of 7-10 nucleotides and only then starts to add nucleotides. It does so in a low-accuracy mode, suggesting that, while the exonuclease is clearly active, it does not contribute to proofreading. The warm-up of the proofreading function is therefore reinterpreted as a switch between two modes of behaviour: a mode 1 of low accuracy in which the 3'----5' exonuclease, while active, is uncoupled from the polymerase and does not contribute to proofreading, and a mode 2 of high accuracy in which the exonuclease is kinetically linked to the polymerase activity.