The paper focuses on the efficiency of local search in a Hybrid evolutionary algorithm (HEA), with application to optimization problem frequently encountered in electronic imaging. Although HEA can significantly improve the overall performance of evolutionary search, the direct usage of methods of local optimization gives rise to a few performance problems including a noticeable additional cost of fitness evaluations attributed to local search; an excessive waste of computational resources on a particular chromosome that is later discarded by the global search; and a possible convergence to a sub-optimal solution when the actual distance from the global optimum is not sufficiently small for the local search to successfully descend to the minimum point. Computational performance of local search can be potentially improved by applying the following techniques: using direct search that can better accommodate shape irregularities of fitness function; adding randomness and periodically re-positioning the search, thus preventing it from converging to a sub-optimal point; creating a tree-like structure for each local neighborhood that keeps track of the explored search space; using cyclic vs. complete local search, thus cutting down the excessive cost attributed to discarded chromosomes; incorporating image response analysis and providing the algorithm with a means of deriving problem-specific knowledge that speeds up the solution. A two-phase cyclic local search is proposed that incorporates these techniques. A series of computational experiments with 2-dimensional grayscale images provide experimental support for the proposed approach and show that computational performance of local search in imaging optimization with HEA can be significantly improved.