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Because of increased emissions of greenhouse gases oceans are warming, causing sea level to rise as the density of seawater falls. Predicting the rates of steric expansion is challenging because of the natural variability of the ocean and because observations are insufficient to adequately cover the ocean basins. Here, we investigate the ability of one ocean reanalysis, two objective analyses, and one combination of satellite geodetic measurements to accommodate data gaps and to reconstruct typical patterns of the steric sea level variability at interannual and multidecadal time scales. Six climate indices are used to identify robust features of the internal variability, using a Least Absolute Shrinkage and Selection Operator (LASSO) regression to select significant predictors of the steric variability. Spatially consistent fingerprints are revealed for all climate indices in the ocean reanalysis dataset, allowing the recovery of most of the steric variability observed in the tropical and North Pacific, as well as large fractions of the Atlantic and Indian Ocean signals. Robust climate mode fingerprints are also identified with high spatial resolution but limited temporal coverage in the geodetic observations. The objective analyses fail to detect many of the patterns expected from climate modes, especially before the Argo era. Climate indices constitute valuable yet underexploited tools to assess the performance of different techniques to reconstruct steric sea levels at interannual and multidecadal scales. Such progress will increase confidence in the historical reconstructions of steric sea levels, which is necessary to improve the closure of regional and global sea level budgets and to validate the predictions of climate models. [ABSTRACT FROM AUTHOR]