We handle in this paper three dominating clique problems, namely, the decision problem itself when one asks if there exists a dominating clique in a graph G and two optimization versions where one asks for a maximum- and a minimum-size dominating clique, if any. For the three problems we propose optimal algorithms with provably worst-case upper bounds improving existing ones by (D. Kratsch and M. Liedloff, An exact algorithm for the minimum dominating clique problem, The- oretical Computer Science 385(1-3), pp. 226-240, 2007). We then settle all the three problems in sparse and dense graphs also providing improved upper running time bounds.