  We model millisecond pulsars winds colliding with radiatively-driven
companion winds in black widow and redback systems. For the redbacks, the
geometry of this intrabinary shock (IBS) is quite sensitive to the expected
equatorial concentration in the pulsar outflow. We thus analytically extend IBS
thin-shock models to $\sim \sin^{2n}\theta$ pulsar winds. We compute the
synchrotron emission from such shocks, including the build-up and cooling of
the particle population as it accelerates along the IBS. For reasonable
parameters, this IBS flux dominates the binary emission in the X-ray band. The
modeling shows subtle variation in spectrum across the IBS peak, accessible to
sensitive X-ray studies. As example applications, we fit archival CXO/XMM data
from the black widow pulsar J1959+2048 and the redback PSR J2339-0533, finding
that the model reproduces well the orbital light curve profiles and energy
spectra. The results show a very hard injected electron spectrum, indicating
likely dominance by reconnection. The light curve fitting is sensitive to the
geometric parameters, including the very important orbital inclination $i$.
Coupled with optical fits of the companion star, such IBS X-ray light curve
modeling can strongly constrain the binary geometry and the energetics of the
MSP wind.
