Deutzia

I have inherited what looks like a very old Deutzia. It is quite dense and I mainly keep it for the Sparrows to find cover from Sparrowhawks as the sparrows' feeding stations are close by. However, this bush rarely flowers and has a lot of tired old growth and what looks like quite an amount of dead wood. I would like to prune it, but not too severely, in the hope that it might flower. I'm thinking of removing the dead wood down to ground level and trimming those branches, with leaves, down by a foot or two. Does anyone have any suggestions. I'm not sure that it is in a good situation but it would be impossible to move it, and its main purpose is for the birds.