Tuned sloshing dampers (TSDs) are the most popular method of structural control to reduce the wind-induced motion of tall buildings. A TSD consists of a tank that is partially filled with a liquid that can slosh. As tower heights increase, their natural frequencies decrease, and to ensure proper tuning the water depths in the TSD tanks become quite shallow. Shallow-water sloshing is very nonlinear, which presents considerable challenges to TSD design. Specifically, as the response amplitude of the liquid sloshing increases during large wind excitation events, the sloshing fluid exhibits a ‘hardening-spring’ behaviour, in which the natural sloshing frequency appears to increase. This phenomenon leads to detuning of the TSD from the structure, and potentially severe performance degradation. The hardening-spring response is produced by the nonlinear modal coupling, which excites many higher order sloshing modes in a shallow tank. This study investigates the performance of a TSD equipped with a flat baffle plate to de-couple the higher order modes from the fundamental sloshing mode. The baffle alters the sloshing frequencies and mode shapes of the higher order modes and reduces the energy transfer to them, while negligibly affecting the response of the fundamental sloshing mode that is responsible for controlling the tower response. The performance of the baffled TSD is evaluating by considering a tower equipped with a traditional shallow-water TSD and a shallow-water TSD with a baffle plate. Nonlinear fluid modelling shows that the nonlinear coupling is reduced, and the motion reduction performance of the TSD is improved.