Two novel data-hiding schemes for secure data communications are presented. These two schemes perform on the pixel differences between the original (host) image and the decompressed image, which is inspired from Wu's and Chao's methods. The first scheme, referred to as 'scheme-1', utilises the differences between two similar images and then embeds the secret data into the different parts. In the embedding process, two auxiliary techniques, zero-replacement and complement-bit, will also be incorporated. In addition, to enhance the hiding efficiency of scheme-1, the authors have followed the bit-plane hiding strategy and created scheme-2. The proposed schemes have two advantages. First, the error distortion can be measured before the hiding process begins. Second, there is no complex computation, which means the hiding process can be executed very efficiently. The experimental results show that the two proposed schemes can achieve better image quality than other data-hiding schemes. At the same time, the new schemes can also satisfy the three basic requirements a data hiding scheme should live up to: invisibility, capacity and data security.