Abstract One of the most useful models in population genetics is that of a selective sweep and the consequent hitch-hiking of linked neutral alleles. While variations on this model typically assume constant population size, many instances of strong selection and rapid adaptation in nature may co-occur with complex demography. Here we extend the hitch-hiking model to evolutionary rescue, where adaptation and demography not only co-occur but are intimately entwined. Our results show how this feedback between demography and evolution determines – and restricts – the genetic signatures of evolutionary rescue, and how these differ from the signatures of sweeps in populations of constant size. In particular, we find rescue to harden sweeps from standing variance or new mutation (but not from migration), reduce genetic diversity both at the selected site and genome-wide, and increase the range of observed Tajima’s D values. For a given initial rate of population decline, the feedback between demography and evolution makes all of these differences more dramatic under weaker selection, where bottlenecks are prolonged. Nevertheless, it is likely difficult to infer the co-incident timing of the sweep and bottleneck from these simple signatures, never-mind a feedback between them. Temporal samples spanning contemporary rescue events may offer one way forward.