Compared with face recognition, the performance of person re-identification (re-ID) is still far from practical application. Among various interferences, there are two factors seriously limiting the performance improvement, i.e., the feature discriminability determined by "external network effectiveness", and the image quality determined by "internal background clutters". Target at the "external network effectiveness" problem, feature pyramids are effective to learn discriminative features because they can learn both detailed features from high-resolution shallow layers and semantical features from low-resolution deep layers, however, it can only achieve slight improvement on re-ID tasks because of the error back propagation problem. To handle the problem and utilize the effectiveness of feature pyramids, we propose a strategy called Feature Pyramid Optimization (FPO). Instead of concatenating features directly, the selected layers are optimized independently in a top-bottom order. Target at the "internal background clutters" problem, background suppression is generally considered for removing the environmental interference and improving the image quality. Several mask-based methods are used attempting to totally remove background clutters but achieve limited promotion because of the mask sharpening effect. We propose a novel strategy, i.e., Gradual Background Suppression (GBS) to reduce the background clutters and keep the smoothness of images simultaneously. Extensive experiments have been conducted and the results demonstrate the effectiveness of both FPO and GBS.