The width of a tree decomposition is the maximal number of constraints associated with each node. If this width is bounded by a constant, a problem equivalent to the original one can be built in polynomial time. The variables that are not associated to a node but are in the scope of the constraints of the node are "projected out" when building this instance. This can be done by first projecting the constraints over the variables of the node and then finding all solutions to this subproblem, or by first solving the subproblem with all constraints and then removing the extra variables.