In this paper, we propose the elimination of dependencies to convert a given dependency quantified Boolean formula (DQBF) to an equisatisfiable QBF. We show how to select a set of dependencies to eliminate such that we arrive at a smallest equisatisfiable QBF in terms of existential variables that is achievable using dependency elimination. This approach is improved by taking so-called don't-care dependencies into account, which result from the application of dependency schemes to the formula and can be added to or removed from the formula at no cost. We have implemented this new method in the state-of-the-art DQBF solver HQS. Experiments show that dependency elimination is clearly superior to the previous method using variable elimination.
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