Knowledge of sulfur dioxide layer height (SO2 LH) is important to understand volcanic eruption processes, the climate impact of SO2 emissions and to mitigate volcanic risk for civil aviation. However, the estimation of SO2 LH from ground-based instruments is challenging in particular for rapidly evolving and sustained eruptions. Satellite wide-swath nadir observations have the advantage to cover large-scale plumes and the potential to provide key information on SO2 LH. In the ultraviolet, SO2 LH retrievals leverage the fact that, for large SO2 columns, the light path and its associated air mass factor (AMF) depends on the SO2 absorption (and therefore on the vertical distribution of SO2), and SO2 LH information can be obtained from the analysis of measured back-scattered radiances coupled with radiative transfer simulations. However, existing algorithms are mainly sensitive to SO2 LH for SO2 vertical columns of at least 20 DU. Here we develop a new SO2 LH algorithm and apply it to observations from the high-spatial-resolution TROPOspheric Monitoring Instrument (TROPOMI). It is based on an SO2 optical depth look-up table and an iterative approach. The strength of this scheme lies in the fact that it is a Covariance-Based Retrieval Algorithm (COBRA; Theys et al., 2021). This means that the SO2-free contribution of the measured optical depth is treated in an optimal way, resulting in an improvement of the SO2 LH sensitivity to SO2 columns as low as 5 DU, with a precision better than 2 km. We demonstrate the value of this new data through a number of examples and comparison with satellite plume height estimates (from IASI and CALIOP), and back-trajectory analyses. The comparisons indicate an SO2 LH accuracy of 1–2 km, except for some difficult observation conditions, in particular for optically thick ash plumes or partially SO2-filled scenes.