Compressed video is a target for researchers looking for a secured, robust, reliable, and reversible data hiding techniques. This paper proposes a novel method for hiding data, which is capable of embedding the bits in each candidate MPEG motion vectors. In this method a displacement lookup table is used to embed the secret message (watermarks,signatures, etc.,). The secret message is organized into a stream of three-bit groups then statistically analyzed with histogram. A three-bit distribution at the encoder side is used to build a lookup table of the displacements to the motion vectors with the design objective of minimizing the displacement changes. The associated macro-block prediction error is calculated to decide which motion vectors should be selected for insertion and extraction of the data. These motion vectors are called candidate motion vectors. The proposed algorithm is tested by embedding the payload (message) at the encoder side in the predictive (P)-frames and successfully extracting it again at the decoder side. The performance is analyzed in terms of peak signal-to-noise ratio (PSNR) and the file size increase of the reconstructed video versus the embedded payload. The results show that the payload of that hidden data is increased compared to other methods using the motion vectors for data hiding. The results for peak signal to noise ratio (PSNR) against the payload give that there is a slight degradation (-2dB) compared to other methods but this degradation is compensated by the decoder.