Volcanic emissions of sulfur dioxide (SO2) affect the environment, climate, and society. Their detection and quantification rely extensively on remote sensing techniques, which are used to track SO2 and monitor volcanic activity worldwide. In particular, nadir-viewing satellites measuring total SO2 vertical column densities (VCDs) have provided valuable insights into volcanic emissions for decades. However, the determination of the SO2 layer height (LH) is more challenging. In this study, we present an improved SO2 LH (and VCD) retrieval algorithm, applicable to the second UV spectral band (BD2) of the TROPOspheric Monitoring Instrument (TROPOMI). This band exhibits a stronger SO2 absorption than the third band (BD3) that is traditionally used for SO2 retrievals. To assess the impact of various spectral, atmospheric, and observation conditions, we conducted sensitivity analyses from a set of synthetic spectra representative of TROPOMI measurements using the Look-Up Table COvariance-Based Retrieval Algorithm (LUT-COBRA). Our results demonstrate that BD2 retrievals result in more accurate estimates of the SO2 heights and columns, particularly in the upper troposphere and lower stratosphere (UTLS), with LH errors reduced by at least a factor of 2. The algorithm was applied to real TROPOMI observations of volcanic eruptions and degassing episodes, and compared to BD3 retrievals. BD2 shows an improved sensitivity, with less noise, and a detection limit as low as 2 DU, surpassing the current operational TROPOMI SO2 product by an order of magnitude. Furthermore, our plume height estimates align closely with independent measurements from the Infrared Atmospheric Sounding Interferometer (IASI) and Microwave Limb Sounder (MLS), confirming the reliability of the approach.