Domination parameters and added matchings

We consider the augmentation problem of how domination parameters behave when a perfect matching P of the complement is added to the graph. We focus on the case that the graph is a tree, and inter alia show that if T is a tree of even order n that is not a star, then T+P has domination number at most 2n/5, independent domination number at most n/2-1, and total domination and upper domination number at most n/2. Further, there exists a choice of P such that T+P has total domination number at most n/3. All these bounds are sharp.