Rapid ice mass variations within the large polar ice sheets lead to distinct and highly non-uniform sea-level changes that have come to be known as ‘sea-level fingerprints’. We explore in detail the physics of these fingerprints by decomposing the total sea-level change into contributions from radial perturbations in the two bounding surfaces: the geoid (or sea surface) and the solid surface. In the case of a melting event, the sea-level fingerprint is characterized by a sea-level fall in the near-field of the ice complex and a gradually increasing sea-level rise (from 0.0 to 1.3 times the eustatic value) as one considers sites at progressively greater distances (up to ≈ 90° or so) from the ice sheet. The far-field redistribution is largely driven by the relaxation of the sea-surface as the gravitational pull of the ablating ice sheet weakens. The near-field sea-level fall is a consequence of both this relaxation and ocean-plus-ice unloading of the solid surface. We argue that the fingerprints provide a natural explanation for geographic variations in sea-level (e.g., tide gauge, satellite) observations. Therefore, they furnish a methodology for extending traditional analyses of these observations to estimate not only the globally averaged sea-level rate but also the individual contributions to this rate (i.e., the sources).