This was a fairly simple image to manipulate, but the technique works quite well for images that have very fine detail on the edges, especially hair. It takes some work and experimentation, but it can be done. If you do have very fine detail, it may be better not to clamp the levels quite so hard as I did here, as a bit of translucency is desired in that case.

One other technique you can try is to use the dodge and burn tools on the edges of the matte. Set the Dodge tool's range to "highlights" and the Burn tool's range to "shadows", reduce the Exposure to around 20%, and brush each tool lightly over the edge. Since you've restricted the range, the dodge will act only to lighten the lights, and the burn to darken the darks. You can get a more subtle edge with this method, though if you apply it several times, you'll wind up with the same kind of 1-bit (two values: black or white) matte I just demonstrated.