  X-ray polarization from the Imaging X-ray Polarimetry Explorer (IXPE)
provides an important new probe of the geometry of the pulsar emission zone and
of particle acceleration in the surrounding pulsar wind nebula (PWN). However,
with IXPE's modest ~20-30" spatial resolution, separation of the pulsar signal
from the nebula is a challenge. Conventional analysis defines an "off" phase
window as pure nebular emission and subtracts its polarization to isolate the
phase-varying pulsar ("on-off fitting"). We present a more sensitive scheme
that uses external measurements of the nebula structure and pulsar light curve
to isolate their contributions to the phase- and spatially-varying polarization
via least-squares regression ("simultaneous fitting"). Tests with simulation
data show ~30% improvement in pulse phase polarization uncertainties, decreased
background systematics, and substantially improved nebular polarization maps.
Applying "simultaneous fitting" to early IXPE Crab data extracts additional
phase bins with significant polarization. These bins show interesting
departures from the well-known optical polarization sweeps, although additional
exposure will be needed for precise model confrontation.
