A roll (10) of glass ribbon (20), having a thickness of 0.3 mm or less, wherein a thickness compliant material interlayer (40) is wound together with the glass ribbon. The characteristics of the interlayer are chosen to form the roll with minimal lateral offset (9). For example, the static coefficient of friction between the interlayer and the glass ribbon may be greater than or equal to 3.0 (as measured with a vertical force of 0.5 N). Other characteristics may include the width, thickness, and compliance, of the interlayer. There is also disclosed a method of rolling a glass ribbon wherein the roll winding parameters, for example web tension and pressure between the layers of the roll, are chosen to minimize the lateral offset.