A jaw for clamping a wheel rim in a tyre changing apparatus provided with a wheel-holder unit having a head, the jaw comprising a top surface, a first lateral surface, a second lateral surface, a bottom surface and a body, extending along a longitudinal orientation between a first end and a second end, the body including: - a connecting portion configured to be connected to the head of the wheel-holder unit; - a base portion extending along the longitudinal orientation; - a first abutment wall, extending radially from the base portion along a clamping orientation, perpendicular to the longitudinal orientation, between a first end and a second end in a spacing-apart direction, and along a transverse orientation, the transverse orientation being perpendicular to the longitudinal orientation and to the clamping orientation; the spacing-apart direction being oriented from the bottom surface to the top surface of the jaw; - a second abutment wall extending from the base portion along the clamping orientation in the spacing-apart direction, along the transverse orientation and longitudinally spaced from the first abutment wall by a working distance; - an abutment surface, longitudinally interposed between the first abutment wall and the second abutment wall and smoothly connected thereto to delimit the body in the spacing-apart direction, between the first abutment wall and the second abutment wall, wherein the abutment surface comprises a first portion, smoothly connected to the first abutment wall, and a second portion (251B, 251C), smoothly connected to the first portion and to the second abutment wall and including an inclined portion inclined relative to the first portion and relative to the longitudinal orientation, wherein the second portion of the abutment surface is located at an advanced position relative to the first portion in the spacing-apart direction of the clamping orientation, to come into contact with the wheel rim, characterized in that the second portion is spaced from the first abutment wall along the longitudinal orientation by a first abutment distance, greater than 30% of the working distance. - a connecting portion configured to be connected to the head of the wheel-holder unit; - a base portion extending along the longitudinal orientation; - a first abutment wall, extending radially from the base portion along a clamping orientation, perpendicular to the longitudinal orientation, between a first end and a second end in a spacing-apart direction, and along a transverse orientation, the transverse orientation being perpendicular to the longitudinal orientation and to the clamping orientation; the spacing-apart direction being oriented from the bottom surface to the top surface of the jaw; - a second abutment wall extending from the base portion along the clamping orientation in the spacing-apart direction, along the transverse orientation and longitudinally spaced from the first abutment wall by a working distance; - an abutment surface, longitudinally interposed between the first abutment wall and the second abutment wall and smoothly connected thereto to delimit the body in the spacing-apart direction, between the first abutment wall and the second abutment wall, wherein the abutment surface comprises a first portion, smoothly connected to the first abutment wall, and a second portion (251B, 251C), smoothly connected to the first portion and to the second abutment wall and including an inclined portion inclined relative to the first portion and relative to the longitudinal orientation, wherein the second portion of the abutment surface is located at an advanced position relative to the first portion in the spacing-apart direction of the clamping orientation, to come into contact with the wheel rim, characterized in that the second portion is spaced from the first abutment wall along the longitudinal orientation by a first abutment distance, greater than 30% of the working distance.