An adjustment mechanism to adjust a telescope sighting system comprises an adjusting muff rotatably supported on a connector part to drive the adjustment mechanism. The connector part is designed to transmit the motion of the adjusting muff to its connected components in order to adjust them. A first interlocking component is linked to the adjusting muff and fitted with first lock elements to constitute a first click array. A display means indicates the excursion of rotation of the adjusting muff, and a switch actuates the displays following a predetermined rotational excursion of the adjusting muff. A second interlocking component linked to the adjusting muff is provided with a second click array--different from the first click array--constituted by second lock components.