Satellite radar altimetry has been providing sea surface heights on an almost global scale for the past 30 years. From this data, an average global mean sea level rise of 3-4 mm per year can be estimated. To determine these small changes with high accuracy, precise and stable measurements are required. Long-term data stability is particularly important for sea-level rise applications. This not only relates to the altimeter measurements themselves, but also to any geophysical correction applied to the data. Furthermore, consistency between different missions is essential to ensure a long time series that is useful for climate studies. This contribution shows how global sea level rise estimates can be affected by geophysical corrections applied to satellite altimetry data and the importance of selecting the right datasets. The focus will be on atmospheric corrections, especially on different wet troposphere path delay corrections derived by models and observations. It will be shown that these corrections can introduce systematic errors in the order of 0.5 mm/year, which is the level of uncertainty currently assumed for the altimetry-derived global mean sea level trend.