Recently, the H.265/HEVC video coding has been standardised by the ITU-T VCEG and the ISO/IEC MPEG. The improvements in H.265/HEVC video coding structure (CTU, motion compensation, inter- and intra-prediction, etc.) open up new possibilities to realise better data hiding algorithms in terms of capacity and robustness. In this paper, we propose a new data hiding method for HEVC videos. The proposed method embeds data in 4 × 4 and some selected larger transform units. As theory of Human Visual System suggests that human vision is less sensitive to change in uneven areas, relatively coarser blocks among the 8 × 8 and 16 × 16 blocks are selected as embedding destinations based on the proposed Jensen-Shannon Divergence and Second Moment (JSD-SM) block coarseness measure. In addition, the SME(1,3,7) embedding technique is able to embed three bits of message by modifying only one coefficient and therefore exhibits superior distortion performance. Furthermore, to achieve better robustness against re-compression attacks, BCH and Turbo error correcting codes have been used. Comparative studies of BCH and Turbo codes show the effectiveness of Turbo codes. Experimental results show that the proposed method achieves greater payload capacity and robustness than many existing state-of-the-art techniques without compromising on the visual quality.