Reversible data hiding is widely used because the host image can be recovered without errors after the extraction of hidden data. One of the popular schemes for reversibility involves the use of prediction-error expansion (PEE). Scholars often modify the basic PEE scheme to hide more secret bits or to improve the quality in stego images. Examples include the pairwise PEE, the difference expansion approach, and others. In our PEE-based method here, by identifying which parts of a prediction error histogram indicate inefficient hiding, we propose increasing the ratio of pixels hiding data to the pixels shifted without hiding data, called the efficiency ratio (ER). We used four tests to improve ER and hence improve the quality of stego images. The basic concept of our method is to check whether an image block or pixel is suitable for embedding data. After deleting the blocks or pixels that are likely to yield erroneous predictions, we can reduce the chance of a high PE. A high PE not only deteriorates the quality of stego images, but also contributes nothing to the embedding capacity. As shown in experiments, our image quality is better than that of many other PEE-based algorithms when similar amounts of data are hidden.