Any good bullet will take a deer, personally limited expansion bullets like the Barnes I would use on an elk or bigger game which I prefer the Lehigh for any way. Your problem may well consist of two parts, the far majority of us put the Power Belts of the bottom of the list of bullets we would use. The spot you aim at and where you hit often has as much to do with a blood trail as the bullet. Hit in the right place with the right bullet a majority of deer will drop on the spot.Just two weeks a go I all most passed on a nice buck because of the angle of the shot, but using 140 gr of Blackhorn and a 40 cal 200gr Lehigh I decided I could do a good job on him he weighted 270 pounds and had a nice 7 point rack I shot him in the back just below the kidney and the bullet torn liver lungs and heart to pieces and he only went 25 yds.
Now normally I would expect a heart shot deer to run a 100yds because that my experience. One the other hand most of them shot right over the heart drop right on the spot. This is the kind of shoot where a really good bullet makes the difference. A Lehigh or a Barns maybe even the most excellently priced Gold Dot.
But I believe that for the most part hitting the right spot is a very large part of having a good blood trail, and that the right spot along with the right bullet and a load of at least 110gr with one of the better powders like Blackhorn [some people prefer 777] will drop them on the spot reliably and so there will be no need to trail. If you can see the deer laying from where he was standing when you shot it takes care of that part of the problem.