Mona, I feel your pain! I have been debating this very issue for months! I concluded that it would not be possible to get the sharp points using Beth Ferrier's method of turned applique by machine - I'm guessing that's the method you're referring to. I paper pieced Month 2, which gave me very satisfying points. Otherwise, though, I think I will have to fold and go with fused applique. Looking ahead to the applique months, there are some pretty small teardrop shapes, and I don't think that turned applique by machine method will work well there either. By hand, sure, but it will be difficult to combine with the paper pieced edges.
I have a photo on my blog of a gorgeous fused applique quilt done by another TQS member, Sandy Lawrence. It was also a Sarah Vedeler design, and Sandy won two major prizes for it. It's the quilt that changed my mind! You can see it here:
http://www.lakeviewstitching.com/2012/03/time-to-get-over-myself.html
And my paper pieced Month 2 is here:
http://www.lakeviewstitching.com/2012/03/paper-piecing-sedona-star-month-2.html
Good luck!