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This paper describes two elitism-based compact genetic algorithms (cGAs)-persistent elitist compact genetic algorithm (pe-cGA), and nonpersistent elitist compact genetic algorithm (ne-cGA). The aim is to design efficient cGAs by treating them as estimation of distribution algorithms (EDAs) for solving difficult optimization problems without compromising on memory and computation costs. The idea is to deal with issues connected with lack of memory by allowing a selection pressure that is high enough to offset the disruptive effect of uniform crossover. The pe-cGA finds a near optimal solution (i.e., a winner) that is maintained as long as other solutions generated from probability vectors are no better. The ne-cGA further improves the performance of the pe-cGA by avoiding strong elitism that may lead to premature convergence. It also maintains genetic diversity. This paper also proposes an analytic model for investigating convergence enhancement.