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Broad-band ocean-bottom seismometer (OBS) deployments present an opportunity to investigate the seafloor sediment thickness, which is important for constraining sediment deposition, and is also useful for subsequent seismological analyses. The Volatile Recycling in the Lesser Antilles (VoiLA) project deployed 34 OBSs over the island arc, fore- and backarc of the Lesser Antilles subduction zone for 15 months from 2016 to 2017. Using the amplitudes and delay times of P-to-S (Ps) scattered waves from the conversion of teleseismic earthquake Pwaves at the crust–sediment boundary and pre-existing relationships developed for Cascadia, we estimate sediment thickness beneath each OBS. The delay times of the Ps phases vary from 0.20 ± 0.06 to 3.55 ± 0.70 s, generally increasing from north to south. Using a single-sediment and single-crystalline crust earth model in each case, we satisfactorily model the observations of eight OBSs. At these stations we find sediment thicknesses range from 0.43 ± 0.45 to 5.49 ± 3.23 km. To match the observations of nine other OBSs, layered sediment and variable thickness crust is required in the earth model to account for wave interference effects on the observed arrivals. We perform an inversion with a two-layer sediment and a single-layer crystalline crust in these locations finding overall sediment thicknesses of 1.75 km (confidence region: 1.45–2.02 km) to 7.93 km (confidence region: 6.32–11.05 km), generally thinner than the initial estimates based on the pre-existing relationships. We find agreement between our modelled velocity structure and the velocity structure determined from the VoiLA active-source seismic refraction experiment at the three common locations. Using the Ps values and estimates from the VoiLA refraction experiment, we provide an adjusted relationship between delay time and sediment equations for the Lesser Antilles. Our new relationship is H=1.42dt$^{1.44}$ , where H is sediment thickness in kilometres and dt is mean observed Ps delay time in seconds, which may be of use in other subduction zone settings with thick seafloor sediments.