Inductive power transmission is widely used to energize implantable microelectronic devices (IMDs), recharge batteries, and energy harvesters. Power transfer efficiency (PTE) and power delivered to the load (PDL) are two key parameters in wireless links, which affect the energy source specifications, heat dissipation, power transmission range, and interference with other devices. To improve the PTE, a 4-coil inductive link has been recently proposed. Through a comprehensive circuit-based analysis that can guide a design and optimization scheme, we have shown that despite achieving high PTE at larger coil separations, the 4-coil inductive links fail to achieve a high PDL. Instead, we have proposed a 3-coil inductive power transfer link with comparable PTE over its 4-coil counterpart at large coupling distances, which can also achieve high PDL. We have also devised an iterative design methodology that provides the optimal coil geometries in a 3-coil inductive power transfer link. Design examples of 2-, 3-, and 4-coil inductive links have been presented, and optimized for a 13.56-MHz carrier frequency and 12-cm coupling distance, showing PTEs of 15%, 37%, and 35%, respectively. At this distance, the PDL of the proposed 3-coil inductive link is 1.5 and 59 times higher than its equivalent 2- and 4-coil links, respectively. For short coupling distances, however, 2-coil links remain the optimal choice when a high PDL is required, while 4-coil links are preferred when the driver has large output resistance or small power is needed. These results have been verified through simulations and measurements.