During the last three decades, at least 30 independent estimates of the secular global mean sea level rise (GMSLR) have been published, based on sufficiently long tide gauge (TG) records. Despite its apparent simplicity, the problem of GMSLR is fraught with a number of difficulties, which make it one of the most challenging questions of climate change science. Not surprisingly, published estimates show considerable scatter, with rates ranging between 1 and 2 mm yr−1 for observations on the century timescale. In previous work, the importance of Glacial Isostatic Adjustment (GIA) upon the assessment of the GMSLR has been clearly demonstrated. In particular, starting from the 1980s, GIA models have been routinely employed to decontaminate TG observations from the effects of melting of the late-Pleistocene ice sheets, to fully highlight the sea level variations driven by climate change. However, uncertainties associated with the Earth’s rheological profile and the time history of the past continental ice sheets can propagate into the GIA corrections. After revisiting previous work and estimates, we suggest a significant modification of the criteria for the selection of the TGs which are most suitable for the robust assessment of the secular GMSLR. In particular, we seek a set of TGs for which GIA corrections are essentially independent of the parametrization of the rheological profile of the Earth’s mantle and of the detailed time chronology of surface loading. This insensitivity is established by considering predictions based upon three GIA models widely employed in the recent literature (namely, ICE–3G, ICE–5G and the one developed at the Research School of Earth Sciences of the National Australian University). Applying this approach and selection criteria previously proposed in the literature, we identify a set of 22 sufficiently evenly distributed TGs. By simple statistical methods, these records yield a ‘preferred’, GIA-independent GMSLR estimate since 1880, namely 1.5 ± 0.1 mm yr−1 (rms = 0.4 mm yr−1, wrms = 0.3 mm yr−1). This value is consistent with various previous estimates based on secular TG observations and with that proposed, for the 20th century, by the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (1.7 ± 0.5 mm yr−1).