Points tend to be a challenge in appliqué, but they need not be. Here's my trick for perfect appliquéed points. The sample shown is done with freezer paper appliqué, but the same principle applies to needleturn.

I begin by basting my seam allowance down a little way away from the point. Just before I get to it, i turn the seam allowance down over the point:

Then fold the right seam allowance over the folded down point:

Fold the left over...

...and hold in place with a basting stitch.

Depending on how wide or narrow your point, you may find you have some extra fabric sticking out at the point. Just leave it for the time being, until you have already sewn the point down.

Take two tiny stitches right at the point, to anchor it down securely. Trim or tuck in (or both) the excess fabric. Finish appliqueing the piece.