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Most studies of late Holocene sea-level changes generally assume stable tectonic conditions. However, unrecognized neotectonic ‘noise’, even the small rates of passive continental margins, can severely distort sea-level reconstructions of the late Holocene. The detailed sea-level curve proposed here is reconstructed by identification of an area (Læsø archipelago in the Kattegat Sea) where small neotectonic level changes and other kinds of ‘background noise’ can be precisely quantified by advanced LiDAR techniques. We show that the absolute (‘eustatic’) sea level of Kattegat has risen by 110±14 cm since AD 1300 and that the Little Ice Age lowstand occurred between 1250 and 1750. Thereafter, four oscillations with a cyclicity of 70 years peaked around 1790, 1860, 1920–1950 (double peak), and at the present. We discuss the global implications of the curve, for example that the acceleration in the present sea-level rise may be part of this 70-year cyclicity, and that the non-anthropogenic sea-level rise between 1700 and 1790 seems faster than the present and projected sea-level rise for the 21st century. Moreover, the conspicuous sea-level fall at the beginning of the Little Ice Age confirms that ice-cap growth can be faster than ice-cap melting. By comparison with 29 long-term tide gauge measurements of the region we show that the isostatic implications of the sea-level curve are in nearly perfect agreement with Peltier's global isostatic VM2 model (applied by IPCC and PSMSL) and yield a 3–4 times smaller spread of isostatic rates. Owing to this higher precision it is possible to produce a reliable isostatic map of SW Scandinavia, Denmark, N Germany and NW Poland. This new map identifies an isostatic jump by 0.6 mm a−1 at the Ringkøbing-Fyn Basement High, separating the isostatic pattern of the North German Basin from the isostatic pattern of the Danish Basin and the Scandinavian Peninsula.