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For difference-expansion (DE)-based reversible data hiding, the embedded bit-stream mainly consists of two parts: one part that conveys the secret message and the other part that contains embedding information, including the 2-D binary (overflow) location map and the header file. The first part is the payload while the second part is the auxiliary information package for blind detection. To increase embedding capacity, we have to make the size of the second part as small as possible. Tian's classical DE method has a large auxiliary information package. Thodi mitigated the problem by using a payload-independent overflow location map. However, the compressibility of the overflow location map is still undesirable in some image types. In this paper, we focus on improving the overflow location map. We design a new embedding scheme that helps us construct an efficient payload-dependent overflow location map. Such an overflow location map has good compressibility. Our accurate capacity control capability also reduces unnecessary alteration to the image. Under the same image quality, the proposed algorithm often has larger embedding capacity. It performs well in different types of images, including those where other algorithms often have difficulty in acquiring good embedding capacity and high image quality.