This paper proposes reversible data hiding using minimum/maximum preserved overflow/underflow avoidance (MMPOUA). The proposed MMPOUA algorithm consists of three main steps. These steps include the minimum (or maximum) pixel fixing, pixel squeezing, and pixel isolation. The aims of pixel fixing are to keep the minimum (or maximum) pixel of a host block unchanged and prevent the occurrence of overflow/underflow. Both the pixel squeezing and pixel isolation supply hiding storage while keeping the amount of distortion low. The proposed method can avoid (or significantly reduce) the overhead bits used to overcome overflow/underflow issues. At an embedding rate of 0.15 bpp, the proposed algorithm can achieve a PSNR value of 48.52 dB, which outperforms several existing reversible data hiding schemes. Furthermore, the algorithm performed well in a variety of images, including those in which other algorithms had difficulty obtaining good hiding storage with high perceived quality.