An adjustable support in the form of a headrest comprises a flexible arm (2) carrying a bifurcated branches (3a). The arm (82) is made up of identical segments (20) that can pivot in relation to each other. A wire (5) holds the arm (2) together and may be loosened by an adjusting mechanism (6) controlled by a knob (9). Partially cylindric surfaces (27, 29) on opposing ends (21, 22) of segments (20) have teeth-like projections extending transversely of the partially cylindric faces (27, 29) for mutual engagement and securing mutual position of adjacent segments (20). The adjustable support is thus able to carry greater loads than prior art adjustable supports.
