If this hedge is deutzia, I would not start by cutting the whole plant down to 2 or 3 feet [7]. Deutzia blooms on old growth, and the recommended time to prune it is immediately after the flowers fade so you do not remove next year’s bloom wood [1, 2, 3, 4, 5].

For a large, woody, overgrown shrub, the better method is usually renewal pruning: remove some of the older stems over a period of years rather than giving the whole shrub a severe heading cut all at once [7]. General pruning guidance for woody shrubs favors light annual thinning cuts over severe heading cuts, because hard cutbacks can spoil the shrub’s natural shape and cause a lot of vigorous, messy regrowth near the cuts [7].

So, my practical recommendation would be:

*  If it has finished flowering, prune it now/immediately after bloom if it is deutzia [1, 2, 3, 4, 5].

*  Use the gradual, over-a-few-years approach rather than cutting the entire hedge down to 2 to 3 feet [7].

*  Reserve a hard renovation cut for a situation where the shrub is truly out of control or needs drastic renewal; when that kind of severe pruning is done, the usual timing is late winter just before budbreak [6, 7].

Because deutzia flowers on old wood, a hard cut that removes most of that older growth also removes much of the plant’s flower potential [1, 2, 3, 4, 5].

There are a few amazing references attached here as hyperlinks.  Please review these to assist you in caring for your deutzia.  Note there are "quick id hints" to help you further identify what variety deutzia you have.  Hope you find this helpful!