A tower structure for a wind energy turbine, wind power, renewable energy, and other uses made of concrete, steel-reinforced concrete or other materials, and a method of manufacture thereof are described. The structure includes several pre-fabricated tower lengths, each tower length having at least three pre-fabricated wedges, such that a central protruding edge of each wedge approaches or lies at a center line of the tower structure when assembled. Tower lengths higher in the tower may be narrower and may be made up of fewer wedges than lower tower lengths. Each tower length may also include several apertures or channels adapted to accommodate a cable joining all the tower lengths of the tower. Also, tower lengths may have a circular or polygonal outer ring made up of bracing elements, each bracing element arranged when assembled to brace one or more wedges.