The control tower of the Alicante airport is 47 m high and is composed of a concrete core, which has elevators, stairs, and a steel structure containing the technical, resting and the air-traffic control rooms. This steel structure is supported by a concrete pole with a tubular section, which is connected at different levels to the concrete core by means of steel trusses. This paper presents results of an investigation on the causes and remedies for vibrations in an air-traffic control tower. It has been shown that wind induced vibrations may disturb air traffic control for acceleration values which are lower than the thresholds as defined in ISO Standards. Besides small differences between theoretical and experimental results, buffeting analysis through numerical methods has proved to be useful to investigate the behaviour of tuned mass dampers and to adjust their design when applied to structures with well defined vibration frequencies.