We don't have a place for a tensioner like Shew noted. The boat came to us with a chain hook that was kept on the ears of the winch we have, but never really kept the anchor tight. I added another chain hook and short line to a cleat (that was already there) just in front of the windlass for cinching the anchor down tight. We use that for keeping the anchor tight up against the front roller when under way. It still sways a little. The tension we get is what we are able to pull on the short piece of line as we are cleating it off. I could maybe get more tension with thinner line that would stretch, but didn't want something too thin that might break at some point... In short, I think I'm basically doing what Willy does but with a chain hook instead of a bowline.
As an extra safety measure we also attach the chain as snug as we can get it but don't put any strain on the winch in the process; just what we can do by hand.
We use the chain exclusively to relieve any strain from the winch when setting the hook. As we are backing down and have deployed our pre-determined amount of chain (before the anchor bites), the hook is put on the chain, and slack added to ensure no strain is taken by the winch/shaft as the anchor bites. (I've since reconfigured the short piece of chain so the loop drops around the after ear of the windlass, it gives a much better angle on hooking the chain for this purpose.)
Once we're set with a bridle and a loop of chain deployed the chain hook is back on for safety, just for the general principle.
Having two hooks, one on a line and one one a chain seems clunky to me, but its working for us for now and seems to be protecting the winch and keeping things redundant for us. Having two of the same hook working the same way is simple at least. At some point we'd like to reconfigure the windlass/bow area to rise the windlass to be in line with the bowsprit and add some storage lockers. At that point we'll probably look to reconfigure how we are securing the anchor when its home...