We present an approach for minimizing the critical current for the magnetization switching in magnetic tunnel junctions by optimizing the spatial distribution of the current density. We show that such a minimization is possible because critical current is determined by the condition of making one of the magnetization eigenstates grow in time. The excitation of the eigenstates is enhanced when the spatial distributions of the eigenstates and current density overlap. Critical current can be viewed as a functional of the current density spatial distribution and it can be minimized by optimizing this distribution. Such an optimization results in a major reduction of the critical current and increase of the switching efficiency, viz. the ratio between the energy barrier and critical current. The minimized critical current increases approximately linearly with the magnetic tunnel junction size, which is much slower than critical current for the case of a uniform current density. The optimized efficiency can be approximately a constant with respect to the magnetic tunnel junction size, which is much higher than the efficiency for the uniform current density. Additional optimization can be achieved by spatially modulating the material parameters, e.g., the saturation magnetization. The presented approach and obtained scaling of the critical current and efficiency offers opportunities for the magnetic tunnel junction optimization.