We present new goodness-of-fit tests for the exponential distribution based on equidistribution type characterizations. For the construction of the test statistics, we employ an L ²-distance between the corresponding V-empirical distribution functions. The resulting test statistics are V-statistics, free of the scale parameter. The quality of the tests is assessed through local Bahadur efficiencies as well as the empirical power for small and moderate sample sizes. According to both criteria, for many common alternatives, our tests perform better than the integral and Kolmogorov-type tests based on the same characterizations.