A three dimensional [3D] video signal (21) comprises a first primary data stream (22) representing a left image to be displayed for the left eye of a viewer and a second primary data stream representing a right image to be displayed for the right eye of the viewer for rendering 3D video data exhibiting a nominal depth range. For enabling overlaying auxiliary image data on the 3D video data at an auxiliary depth in the nominal depth range a secondary data stream (23) is included in the signal. The secondary data stream is displayed, during overlaying, for one of the eyes instead of the respective primary data stream for rendering the 3D video data exhibiting a modified depth range farther away from the viewer than the auxiliary depth.