Near the southern end of Puget Sound, down near the western tip of Squaxin Island, you'll find Hammersley Inlet. But you'll have to look closely.
Peter Puget, on his longboat voyage back in 1792, didn't find it. Sailed right past it, actually. It was another 50 years before American explorer Charles Wilkes finally inked the inlet onto a map. It's got a small entrance, sort of a dog-leg opening off of the wider sound, and it's not hard to see how it might have been overlooked.
It's almost six miles from the mouth to Shelton. Six long, skinny and relatively straight miles from one end to the other. Because it's such a slender waterway and because it's so far down the sound, currents here are often on a par with the Tacoma Narrows. The volume of water running down Hammersley is nowhere near as much as flows through the Narrows, but the fact that the inlet is just a few hundred yards across means that it acts like a virtual fire hose, and the water gets moving through there in a hurry.
Timing your trip to take advantage of the currents is a must. You can launch at either end, in Shelton or at Arcadia, but it would be prudent to base your launch time on when the water is running in the same direction that you want to go. It's a lot more enjoyable that way.
Of course, being such a narrow waterway located so near to the eastern slope of the Olympics means that wind is often a factor. Wind gets funneled down the inlet and often overpowers even the strongest opposing current, which can not only impede a paddler's progress, but it can make for some sporty conditions indeed. Plans have been known to change in situations like this.
Not far from the mouth of Hammersley is Hope Island, a Washington State Park and a very good lunch stop. Or overnight camping spot, for that matter. Camp sites are spacious and easily accessible to paddlers, but fires are not permitted.
Hammersley Inlet is the deep south of Puget Sound, easy to overlook, but worth looking for.