This paper analyses the relationship between the coil design parameters and the system performance, including power transfer efficiency and amount, when circular flat spiral coils are adopted in a wireless power transfer (WPT) system. Coil design variables including outer radius, inner radius, channel width and coil turns are thoroughly studied to improve the system performance with a limited maximum outer radius for practical purposes. A two-coil WPT system has been built to verify the analysis, and the experimental results show good consistency with the theoretical calculations and simulation results, which show that the coil design parameters have a significant impact on the system performance, even with the same coil size. In the experiments, the coil-to-coil distance is 150 mm, the maximum coil outer radius is limited in 300 mm, and the DC input voltage and the load resistance are 100 V and 5 Ω, respectively. When the coils are tightly-wound in the most traditional way to maximize the coil size, the coil-system efficiency is 62.6% with only 4.5 W load power. In contrast, the efficiency optimized coil can improve the coil-system efficiency to 91.2% with the outer radius stayed the same. Besides, when the power transfer efficiency and amount are considered simultaneously, the system can achieve 1279 W load power with 85.94% coil-system efficiency.