Cell imbalance, a notorious but widely found issue, degrades the performance and reliability of large battery packs, especially for cells connected in series where their overall capacity delivery is dominated by the weakest cell. In this paper, we exploit the emerging reconfigurable battery packs to mitigate the cell imbalance via the joint consideration of system reconfigurability and State-of-Health (SoH) of cells. Via empirical measurements and validation, we observe that more capacity can be delivered when cells with similar SoH are connected in series during discharging. Based on this observation, we propose two SoH-aware reconfiguration algorithms focusing on fully and partially reconfigurable battery packs, and prove their (near) optimality in capacity delivery. We evaluate the proposed reconfiguration algorithms analytically, experimentally, and via emulations, showing 10%-60% improvement in capacity delivery when compared with SoH-oblivious approaches, especially when facing severe cell imbalance.