Consolidation refers to the putative process by which existing memories are strengthened over time. There is a widespread consensus within the neuroscientific community that consolidation is an important component of human memory. By contrast, the notion is rarely employed by cognitive modellers. We focus on behavioural data that have frequently been cited in support of consolidation—for example, the Ribot gradient in amnesia and the temporal effects of retroactive interference—and show that (1) those data are in fact problematic for classic consolidation theory and (2) can be explained readily within a cognitive model based on temporal distinctiveness. We suggest that this changes the evidentiary landscape for consolidation and narrows the field of supporting evidence.