I would suggest giving yourself about an inch all the way around the odd-shaped pieces. Rough cut them to the shape you need with the added amount. When I'm in doubt, I will also pin along the seam lines and fold back to make sure it covers the area required. Then go back and sew once I have it worked out.
The only part about paper piecing that I don't like is the added waste. Otherwise, it's a great technique especially for some of those really pointy shapes.