Phasmid,
Outside turning will work, and unlike inside neck reaming has the additional benefit of evening out neck thickness, which may help accuracy.
But if the problem is the "dreaded donut" (and that's that most neck-thickening problems amount to), you must turn the neck all the way down into the beginning of the shoulder. If you haven't turned necks before, it's also easy to turn them down too much, so your sizing die doesn't reduce the neck diameter enough to hold bullets. If you're using collet or bushing dies this isn't a problem, but it can be with standard sizing dies.
If you don't have a neck-turning setup, it will also cost some money. An inside neck reamer is pretty cheap, and will definitely solve the problem.
