Summary: Densely connected distributed constraint optimisation problems (DisCOP) can be difficult to solve optimally, but finding good lower bounds on constraint costs can help to speed up search. We show how good lower bounds can be found by solving relaxed problems obtained by removing inter-agent constraints. We present modifications to the Adopt DisCOP algorithm that allow an arbitrary number of relaxations to be performed prior to solving the original problem. We identify useful relaxations based on the solving structure used by Adopt, and demonstrate that when these relaxations are incorporated as part of the search it can lead to significant performance improvements. In particular, where agents have significant local constraint costs, we achieve over an order of magnitude reduction in messages exchanged between agents. Finally, we identify cases where such relaxation techniques produce less consistent benefits.