A pendulum-type tuned mass damper (TMD) - tuned sloshing damper (TSD) system is proposed as a cost effective device to reduce wind-induced structural motion. Lagrange's principle is employed to develop an equivalent mechanical model for the system. The sloshing liquid provides additional gravitational restoring force to the pendulum TMD, but does not provide a corresponding increase to its inertia. As a result, the natural frequency of the pendulum TMD is increased due to the TSD degree of freedom. Shake table testing is conducted on several pendulum TMD-TSD systems that are subjected to harmonic base excitation at discrete frequencies near the natural frequency of the pendulum TMD. The modelled and experimental results are in reasonable agreement when the liquid is not shallow, or the response amplitude is not large. The pendulum TMD-TSD is coupled to a linear structure and it is demonstrated through an analytical study that the device provides performance that is comparable to a traditional TMD. The proposed system is advantageous because it does not require a viscous damping system that is often one of the most costly components of traditional TMDs.