We consider a fresh-product supply chain (FPSC) in which the supplier and the e-tailer invest in quality-improvement effort and fresh-keeping effort, respectively. One centralized model and two decentralized models are developed to investigate the optimal effort and pricing decisions for double-effort (de), quality-improvement effort only (qe), fresh-keeping effort only (fe) and none effort (ne) strategies, respectively. We also conduct a comparative analysis to find out the superiority among four different strategies, to reveal the effect of different power structures, and to show the distortion of effort decisions. Our research reveals several insights. First, we find that the de strategy is a dominant strategy for both the supplier and the e-tailer. Second, although channel power structures have a significant impact on the effort decisions, it neither guarantees a greater effort nor more profit for the FPSC. Third, the optimal quality-improvement effort and fresh-keeping effort are always distorted in a decentralized setting, and the channel efficiency is lost the most under a de strategy. Finally, we propose the net-revenue and cost sharing contract and the two-part tariff contract to coordinate this decentralized FPSC. We further demonstrate several sensitivity effects based on computational studies, providing additional insights for better understanding the theoretical results.