A method of decoding closed caption disparity data, involves a TV receiver receiving closed caption disparity data for a 3D display encoded as a sequence of frame interval/slope change pairs, with the frame interval representing a designated number of frames over which each linear function representing disparity is to be applied paired with a value indicating a change in slope from the slope of a preceding segment. A first segment in the sequence presumes a predetermined slope as a reference. A sequence of caption data packets specifies a closed caption display window containing closed caption text. The disparity value is used in each frame to determine a horizontal offset of left and right eye views of the CC display that establishes the closed caption display window's perceived z-axis position. This abstract is not to be considered limiting, since other embodiments may deviate from the features described in this abstract.