Frequency reuse improves system capacity but sacrifices cell-edge user equipments (UEs) due to inter-cell interference. To solve this problem, fractional frequency reuse (FFR) was proposed, which ameliorates cell-edge UEs by using a larger reuse factor for them than for cell-center UEs. In this paper, we investigate a common type of FFR schemes, called partial frequency reuse (PFR), and find that cell-edge UEs are not necessarily the worst ones. Instead, UEs on the edge of the inner area may be the worst in many cases. To improve max-min fairness without degrading system capacity, we study several multi-layer PFR schemes. By extensive simulations, we propose a 4-layer scheme with 7-portions of spectrum, which could improve both max-min fairness and system capacity, as long as the inner radius, the reuse factors of different layers, and the ratio of middle and outer areas are carefully designed.