Methods for reversible data hiding are disclosed herein. These methods may be applied to images for reversible image data hiding. In one embodiment, a method for reversible data hiding comprises identifying carrier data having a plurality of components and establishing prediction-errors for each of the components of the carrier data. A first threshold and a second threshold are established. The prediction-errors of the components are evaluated against the first threshold to identify components for possible hiding. The components identified for possible hiding are evaluated against the second threshold to identify components for hiding. To-be embedded data is embedded into the carrier data identified for hiding to create marked data. The marked data is evaluated for overflow or underflow. If overflow or underflow is detected, histogram modification is performed. Marked data is then established.