Adjustable headgear is disclosed which includes a first or occipital strap having an upper end and a lower end and is adapted to extend from the back of the head of the wearer upward to the top area of the head. A second strap having an upper end and a lower end is adapted to extend from the right side of the head of the wearer upward to the top area of the head. A third strap having an upper end and a lower end is adapted to extend from the left side of the head of the wearer upward to the top area of the head. A top adjustment piece has slits therein through which the upper ends of the straps pass so that the length of each strap from its lower end up to the adjustment piece can be adjusted by sliding the strap through the slits in the adjustment piece. Backstrap means has forward end portions connected to the lower ends of the second and third straps and extends around from the lower end of the second strap to the lower end of the third strap. The lower end of the first strap is connected to the strap means generally centrally of the latter.