In the edit window you'll see the initial planar map, but you'll also see the Pelt Stretcher (Fig.16). Click the Simulate Pelt Pulling button a few times until it's close to what you want. You may need to scale the stretcher a few times, depending on the complexity of the pelt.
Close the pelt window, go to Tools > Relax Dialog (Fig.17)
Set it to Relax by Face Angles and click the Apply Button a few times (Fig.18 - 19).
Yay! That's so much easier than doing it manually - enjoy!