A roll of wiping paper is obtained by winding a sheet of multi-ply absorbent paper around a core. The sheet includes at least a first and a second ply of absorbent paper, each with a grammage of between 15 and 30 g/m2 and at least one of the plies incorporating a wet strength additive. The thickness of the sheet Ep being between 0.02 and 0.07 cm, the diameter of the core being less than 3.5 cm, the diameter of the roll being between 4.5 cm and 11 cm for a volume V of absorbent paper per unit length of the roll, and the absorbency A of the sheet in cm3 of water per gram of paper being greater than 6 cm3/g. The ratio E=A/(Ep*V) of the roll is greater than or equal to 3.2.