We construct two U-empirical tests for the logistic location family which are based on appropriate characterization of this family using independent exponential shifts. We study the limiting distributions and local Bahadur efficiency of corresponding test statistics under close alternatives. It turns out that the present tests are considerably more efficient than the recently proposed similar tests based on another characterization. The efficiency calculations are accompanied by the simulation of power for new tests together with the previous ones.Both efficiency and power turn out to be very high. Finally we consider the application of our tests to real data example.