  We present a simple, effective approach for estimating the on-order
backgrounds of spectra taken with the highest-resolution modes of the Space
Telescope Imaging Spectrograph (STIS) on-board the Hubble Space Telescope. Our
scheme for determining the on-order background spectrum uses polynomial fits to
the inter-order scattered light visible in the two-dimensional STIS MAMA
images. We present a suite of high-resolution STIS spectra to demonstrate that
our background subtraction routine produces the correct overall zero point, as
judged by the small residual flux levels in the centers of strongly-saturated
interstellar absorption lines. Although there are multiple sources of
background light in STIS echelle mode data, this simple approach works very
well for wavelengths longward of Lyman-alpha. At shorter wavelengths, the
smaller order separation and generally lower signal-to-noise ratios of the data
can reduce the effectiveness of our background estimation procedure. Slight
artifacts in the background-subtracted spectrum can be seen in some cases,
particularly at wavelengths <1300 Ang. Most of these are caused by echelle
scattering of strong spectral features into the inter-order light. We discuss
the limitations of high-resolution STIS data in light of the uncertainties
associated with our background subtraction procedure. We compare our
background-subtracted STIS spectra with GHRS Ech-A observations of the DA white
dwarf G191-B2B and GHRS first-order G160M observations of the early-type star
HD 218915. We find no significant differences between the GHRS data and the
STIS data reduced with our method in either case.
