Efficiency optimization of dual-Active-bridge (DAB) converters involves the minimization of both conduction and switching losses. However, it is challenging to achieve these two objectives simultaneously due to their conflicting nature, i.e., circulating current is required to realize zero-voltage switching (ZVS) but the presence of an excessive amount of the circulating current is the main cause of conduction loss and low efficiency. This dilemma has been common to conventional DAB converter topologies and modulation schemes which cannot provide sufficient degrees of freedom (DoFs) to the design of their operation modes. This paper is an illustration of the merits of utilizing reconfigurability of the operation mode as a new DoF in designing the operation of DAB converters to minimize both conduction and switching losses. The proposed DAB converter is designed to switch between two operation modes. For 25%-100% of the rated output power, a new modulation scheme based on the four-level ac voltages is proposed to achieve zero circulating current, zero backflow power, and full-range ZVS. Below 25% of the rated output power, the new modulation scheme transitions smoothly to the enhanced dual-phase-shift (EDPS) modulation scheme that continues to achieve zero backflow power and full-range ZVS while the incurred circulating current is moderated by operating the ac voltages at half-Amplitude. The experimental results obtained from a 2-kW prototype show that, in comparison to conventional modulation schemes, the proposed modulation scheme is capable of maintaining the highest efficiency over the full output power range and greatly improves the reliability of switches due to full-range ZVS operation.