Abstract: A curling iron is provided having two handles coupled to two heating tips having non-symmetrical cross-sectional shapes with respect to their lengthwise axes. At least one of the heating tips is rotatably coupled to its handle to rotate along an axis lengthwise along the handle. Thus, by rotating the heating tips about axes along the handle length to orient the heating tip cross-sectional shapes with respect to each other so that various heating tip contact surfaces are selected, the curling iron can be used to (1) curl hair to different curl shapes and tightness, and (2) straighten or flatten hair. Each curling iron handle may also include demountable heating tip and power cord couplings so that wires in the handle can be demountably connected to various heating tips, and can be demountably connected to an electrical power cord for powering the heating element coupled to that handle.