Energy barriers in magnetization reversal dynamics have long been of interest because the barrier height determines the thermal stability of devices as well as the threshold force triggering their dynamics. Especially in memory and logic applications, there is a dilemma between the thermal stability of bit data and the operation power of devices, because larger energy barriers for higher thermal stability inevitably lead to larger magnetic fields (or currents) for operation. Here we show that this is not the case for current-induced magnetic domain-wall motion induced by adiabatic spin-transfer torque. By quantifying domain-wall depinning energy barriers by magnetic field and current, we find that there exist two different pinning barriers, extrinsic and intrinsic energy barriers, which govern the thermal stability and threshold current, respectively. This unique two-barrier system allows low-power operation with high thermal stability, which is impossible in conventional single-barrier systems.