I have to put mine in the dryer first. 15 - 20 min seems to be enough to keep most of the stiffness away. 10 min in the dryer first is not enough, in my experience.
Otherwise, it's got to be a SUPER windy day where the diapers are getting tossed/blown all over the place on the line in order to not use the dryer at all and still have soft diapers. But, we do have really hard water here and I'm pretty sure that's a factor.