The DCOP model has gained momentum in recent years thanks to its ability to capture problems that are naturally distributed and cannot be realistically addressed in a centralized manner. Dynamic programming based techniques have been recognized to be among the most effective techniques for building complete DCOP solvers (e.g., DPOP). Unfortunately, they also suffer from a widely recognized drawback: their messages are exponential in size. Another limitation is that most current DCOP algorithms do not actively exploit hard constraints, which are common in many real problems. This paper addresses these two limitations by introducing an algorithm, called BrC-DPOP, that exploits arc consistency and a form of consistency that applies to paths in pseudo-trees to reduce the size of the messages. Experimental results shows that BrC-DPOP uses messages that are up to one order of magnitude smaller than DPOP, and that it can scale up well, being able to solve problems that its counterpart can not.