  The PIAA is a now well demonstrated high contrast technique that uses an
intermediate remapping of the pupil for high contrast coronagraphy
(apodization), before restoring it to recover classical imaging capabilities.
This paper presents the first demonstration of complete speckle control loop
with one such PIAA coronagraph. We show the presence of a complete set of
remapping optics (the so-called PIAA and matching inverse PIAA) is transparent
to the wavefront control algorithm. Simple focal plane based wavefront control
algorithms can thus be employed, without the need to model remapping effects.
Using the Subaru Coronagraphic Extreme AO (SCExAO) instrument built for the
Subaru Telescope, we show that a complete PIAA-coronagraph is compatible with a
simple implementation of a speckle nulling technique, and demonstrate the
benefit of the PIAA for high contrast imaging at small angular separation.
