Although iceberg meltwater accounts for nearly half of the freshwater release from the Antarctic ice sheet, most ocean models do not represent the vertical distribution of this meltwater in a realistic way. Here, we investigate the importance of distributing the iceberg meltwater vertically in an ocean model that represents icebergs as Lagrangian particles. For more robust estimates, we update the iceberg melting laws: (i) we extend the three-equation formulation used for ice shelf melting to the iceberg basal melt parameterisation, (ii) we adopt a new formulation of lateral iceberg melt in which the buoyant plumes are fed by basal melt, and (iii) we improve the physical consistency of wave-induced ablation in our equations. The updated formulations produce a substantial increase in average lateral melt and a slight reduction in wave-induced ablation and basal melt compared to the pre-existing configuration. Seasonally, lateral melting becomes a major summer contributor, exceeding basal melting in magnitude, and all iceberg melting components decrease in winter. The enhanced sensitivity of wave-induced ablation to sea-ice concentration suppresses iceberg melting near the Antarctic margin, promoting longer iceberg lifetimes. Sensitivity simulations show that even when meltwater is evenly distributed in the vertical down to the iceberg keel depth, 76 % to 87 % of the iceberg meltwater remains injected into the surface mixed layer. Freshwater injection at depth promotes warming and salinification of the Amundsen Sea near the seabed, and freshens and cools the East Antarctic and western Ross Sea continental shelves, but all these changes have a small magnitude. Also, it leads to thinner sea ice and locally enhanced sea-ice production, especially in the southwestern Weddell Sea. Overall, these results imply that, for Southern Ocean-scale responses, modelling studies to date that release iceberg meltwater at the surface can still be considered reliable.