A perpendicular magnetic recording system uses an exchange-spring type of perpendicular magnetic recording medium. The medium has a recording layer (RL) that includes a lower media layer (ML) and a multilayer exchange-spring layer (ESL) above the ML. The high anisotropy field (high-Hk) lower ML and the multilayer ESL are exchange-coupled across a coupling layer. The multilayer ESL has at least two ESLs separated by a coupling layer, with each of the ESLs having an Hk substantially less than the Hk of the ML. The exchange-spring structure with the multilayer ESL takes advantage of the fact that the write field magnitude and write field gradient vary as a function of distance from the write pole. The thicknesses and Hk values of each of the ESLs can be independently varied to optimize the overall recording performance of the medium.