Two different embedding schemes are presented in this paper. One aims to increase rate-distortion performance at low embedding rates. It will increase performance at low embedding rates from the following three main aspects: 1) a local variance-controlled mechanism, 2) a better predictor and 3) a new embedding scheme which can decrease the number of the pixels to be modified on the basis of providing a certain embedding capacity. Since the first scheme is only to provide low embedding rate with high visual quality, another scheme is designed to achieve higher embedding rate with good visual quality. In the second scheme, the center pixel of a three-pixel set is the prediction of a pixel, and thus any modification to it is meaningless. Each three-pixel set contains two differences. Based on the fact that the center pixel can not be modified, the remaining two pixels must be modified so that both of difference are shifted by 1. For instance, if both of pixels can carry 1-bit watermark and to-be-embedded bits are both 1, then two pixels must be shifted left or right by 1. Since we can not shift two difference by modifying only the center pixel, the distortion is high. To decrease distortion, the possibility that two bits are both equal to 1 is discarded in this paper. Experimental results also demonstrate the proposed method is effective.