  We present new consistent goodness-of-fit tests for exponential distribution,
based on the Desu characterization. The test statistics represent the weighted
$L^2$ and $L^{\infty}$ distances between appropriate V-empirical Laplace
transforms of random variables that appear in the characterization. In
addition, we perform an extensive comparison of Bahadur efficiencies of
different recent and classical exponentiality tests. We also present the
empirical powers of new tests.
