  Let K denote a finite extension of Qp. We give necessary and sufficient
conditions for an infinite totally wildly ramified extension L/K to be strictly
APF in the sense of Fontaine-Wintenberger. Our conditions are phrased in terms
of the existence of a certain tower of intermediate subfields. These conditions
are well-suited to producing examples of strictly APF extensions, and in
particular, our main theorem proves that the phi-iterate extensions previously
considered by the first two authors are strictly APF.
