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In reversible data hiding (RDH) schemes, how to select those smooth pixels, pixel pairs or pixel blocks in order to improve performance is an important issue. For pixel-value-ordering (PVO) based RDH schemes, two existing techniques appear to be defective since only two reference pixels in a block or the right and bottom neighbors of a block are exploited as the context for block selection, and their performance might be only adequate for those smooth images. For rough images, the embedding performance could be affected. In this paper, an efficient block selection method by computing a block’s smoothness with a full-enclosing context (FEC) way is proposed. Obtained results show that the proposed FEC strategy can better estimate a block’s smoothness for PVO-based schemes. Furthermore, a more scalable pairing way is presented for the recently reported location-based PVO predictor. The proposed PVO scheme can be implemented by dividing the cover image and embedding bits into two different types of blocks, respectively. Experimental results show that the marked images by the proposed two-stage PVO scheme have higher visual quality, e.g., the average PSNR for the Kodak image database is 63.31 dB after embedding 10,000 bits, and the gain is 0.16 dB against the best result in the literature. Compared with some state-of-the-art RDH works, the superiority of the proposed algorithm has been verified in extensive experiments. [ABSTRACT FROM AUTHOR]