Use of highly concentrated methanol fuel is required for direct methanol fuel cells (DMFCs) to compete with the energy density of Li-ion batteries. Because one mole of H2O is needed to oxidize one mole of methanol (CH3OH) in the anode, low water crossover to the cathode or even water back flow from the cathode into the anode is a prerequisite for using highly concentrated methanol. It has previously been demonstrated that low or negative water crossover can be realized by the incorporation of a low-α membrane electrode assembly (MEA), which is essentially an MEA designed for optimal water management, using, e.g. hydrophobic anode and cathode microporous layers (aMPL and cMPL). In this paper we extend the low-α MEA concept to include an anode transport barrier (aTB) between the backing layer and hydrophobic aMPL. The main role of the aTB is to act as a barrier to CH3OH and H2O diffusion between a water-rich anode catalyst layer (aCL) and a methanol-rich fuel feed. The primary role of the hydrophobic aMPL in this MEA is to facilitate a low (or negative) water crossover to the cathode. Using a previously developed 1D, two-phase DMFC model, we show that this novel design yields a cell with low methanol crossover (i.e. high fuel efficiency, ∼80%, at a typical operating current density of ∼80–90% of the cell limiting current density), while directly feeding high concentration methanol fuel into the anode. The physics of how the aTB and aMPL work together to accomplish this is fully elucidated. We further show that a thicker, more hydrophilic, more permeable aTB, and thicker, more hydrophobic, and less permeable aMPL are most effective in accomplishing low CH3OH and H2O crossover.