Several components of the Earth system are at high risk of undergoing rapid, irreversible qualitative changes or “tipping” as climate warming increases. Therefore, it is necessary to investigate the feasibility of halting or even reversing the crossing of tipping thresholds. Here, we study feedback control of an idealized energy balance model (EBM) for Earth’s climate that exhibits a “small ice sheet” instability that is responsible for a rapid transition to an ice-free climate under increasing greenhouse gas pressures. We develop an optimal control strategy for the EBM under different forcing scenarios to reverse sea ice loss while minimizing costs. Control is achievable for this system, but the cost increases nearly fourfold when the system tips over. While thermal inertia can delay tipping, leading to a critical forcing threshold being crossed, this freedom comes with a steep increase in the control required once tipping occurs. Furthermore, we found that optimal control is localized in the polar region. (Parvathi Kooloth, Jian Lu, Adam Rupe, more at nature.com)