A band adapted to be worn on a limb of a person or animal includes a fabric member and an elastic member attached to the fabric member. A first half of a fastening system is attached to an inner surface of the elastic member, and a second half of the fastening system is attached to the fabric member on the outer surface thereof only around a portion of its perimeter so as to define a space between the outer surface of the fabric member and the second half of the fastening system, the space adapted to be used as a pocket. The band is adjustable to accommodate limbs of various sizes by adjusting a position along the second half of the fastening system where the first half of the fastening system is detachably connected.