Timepiece with dial having a rotary index

A timepiece comprising

• a frame defining a housing designed to receive a timepiece movement, and
• a dial positioned on the frame and defining a plane, the dial including at least one opening, dimensioned so as to leave visible at least one index mounted rotationally on the frame along an axis essentially perpendicular to the plane of the dial and having a display surface situated on the dial side, oriented along a plane essentially parallel to that of the dial,
• a fitting positioned so as to partially cover the display surface and divide it into a first hidden portion and a second visible portion,
• the timepiece comprises a control member, associated with kinematic transmission means connecting the control organ and the index, such that an action on the control organ drives the rotation of the rotary index, so that the first portion (20a) becomes hidden and at least the main part of the second portion (20b) becomes visible,
• wherein the display surface of the index can be arranged at a level selected from:
• a level where said display surface is flush with the upper surface of the dial, and
• a level where said display surface is situated at a slightly higher level relative to the visible surface of the dial.