A method for adjusting a tape wrap angle is described comprising the steps of operating the tape system to generate or regenerate an electrical signal in the head from the tape, either increasing or reducing the tape wrap angle as appropriate until a signal from the tape head reappears or goes to zero, then increasing the wrap angle until the desired angle is achieved as measured by the signal from the head or by moving the tape support a fixed amount. A tape recording and/or reading system with adjustable wrap angles is described which can be used with a method of the invention. The system includes one or more rollers mounted on an adjustable shaft with an eccentric or axially offset portion supporting the roller. Preferably for a magnetic head, an adjustable shaft and roller are located on the tape-in and tape-out side of the tape head. The angular orientation of the eccentric shaft is adjustable, thereby, allowing precise adjustment of the position of the roller with respect to the tape head. Rotating the shaft moves the eccentric portion of the shaft further behind or closer to the head and, therefore, causes the roller mounted on the eccentric portion of the shaft to move similarly resulting in a change in the corresponding wrap angle of the tape in relation to the head. When the desired wrap angle is achieved, the shaft can be restrained from further rotation by an appropriate friction or other locking means. Although the invention can be used with any type of tape head, it is used to particular advantage with flat contour tape recording heads.