Many agent coordination problems can be modeled as distributed constraint optimization (DCOP) problems. ADOPT is an asynchronous and distributed search algorithm that is able to solve DCOP problems optimally. In this paper, we introduce Iterative Decreasing Bound ADOPT (IDB-ADOPT), a modification of ADOPT that changes the search strategy of ADOPT from performing one best-first search to performing a series of depth-first searches. Each depth-first search is provided with a bound, initially a large integer, and returns the first solution whose cost is smaller than or equal to the bound. The bound is then reduced to the cost of this solution minus one and the process repeats. If there is no solution whose cost is smaller than or equal to the bound, it returns a cost-minimal solution. Thus, IDB-ADOPT is an anytime algorithm that solves DCOP problems with integer costs optimally. Our experimental results for graph coloring problems show that IDB-ADOPT runs faster (that is, needs fewer cycles) than ADOPT on large DCOP problems, with savings of up to one order of magnitude.