Changes in mean sea level (MSL) are a major, but not the unique, cause of changes in high-percentile sea levels (HSL), e.g. the annual 99.9th quantile of sea level (among other factors, climate variability may also have huge influence). To unravel the respective influence of each contributor, we propose to use structural time series models considering six major climate indices (CI) (Artic Oscillation, North Atlantic Oscillation, Atlantic Multidecadal Oscillation, Southern Oscillation Index, Niño 1+2 and Niño 3.4) as well as a reconstruction of MSL. The method is applied to eight century-long tide gauges across the world (Brest (France), Newlyn (UK), Cuxhaven (Germany), Stockholm (Sweden), Gedser (Danemark), Halifax (Canada), San Francisco (US), and Honolulu (US)). The treatment within a Bayesian setting enables to derive an importance indicator, which measures how often the considered driver is included in the model. The application to the eight tide gauges outlines that MSL signal is a strong driver (except for Gedser), but is not unique. In particular, the influence of Artic Oscillation index at Cuxhaven, Stockholm and Halifax, and of Niño Sea Surface Temperature index 1+2 at San Francisco appear to be very strong as well. A similar analysis was conducted by restricting the time period of interest to the 1st part of the 20th century. Over this period, we show that the MSL dominance is lower, whereas an ensemble of CI contribute to a large part to HSL time evolution as well. The proposed setting is flexible and could be applied to incorporate any alternative predictive time series such as river discharge, tidal constituents or vertical ground motions where relevant.