An approach to the computation of Bahadur Efficiency was proposed by Bahadur and Raghavachari in their paper in Proceedings of Sixth Berkeley Symposium. The objective of the paper is to exhibit this approach to the Computation of Hodges-Lehmann efficiency for a few examples. Many of the examples are new and these indicate the power of the method which does not entail the Computation of the tail probabilities for the distribution of the test statistic under a specific alternative. Examples include tests relating to normal, poisson, correlation, coefficient, multiple correlation, coefficient and rank tests for one sided distributions.