  Spectropolarimetric measurements at moderate spectral resolutions are
effective tracers of stellar magnetic fields and circumstellar environments
when signal to noise ratios (SNRs) above 2000 can be achieved. The LRISp
spectropolarimeter is capable of achieving these SNRs on faint targets with the
10m aperture of the Keck telescope, provided several instrumental artifacts can
be suppressed. We describe here several methods to overcome instrumental error
sources that are required to achieve these high SNRs on LRISp. We explore high
SNR techniques such as defocusing and slit-stepping during integration with
high spectral and spatial oversampling. We find that the instrument flexure and
interference fringes introduced by the achromatic retarders create artificial
signals at 0.5\% levels in the red channel which mimic real stellar signals and
limit the sensitivity and calibration stability of LRISp. Careful spectral
extraction and data filtering algorithms can remove these error sources. For
faint targets and long exposures, cosmic ray hits are frequent and present a
major limitation to the upgraded deep depletion red-channel CCD. These must be
corrected to the same high SNR levels, requiring careful spectral extraction
using iterative filtering algorithms. We demonstrate here characterization of
these sources of instrumental polarization artifacts and present several
methods used to successfully overcome these limitations. We have measured the
linear to circular cross-talk and find it to be roughly 5\%, consistent with
the known instrument limitations. We show spectropolarimetric signals on brown
dwarfs are clearly detectable at 0.2\% amplitudes with sensitivities better
than 0.05\% at full spectral sampling in atomic and molecular bands. Future
LRISp users can perform high sensitivity observations with high quality
calibration when following the described algorithms.
