  Recent results from the ROSAT All-Sky Survey (RASS) have shown that broad
absorption line (BAL) QSOs are either highly absorbed or underluminous in the
soft X-ray bandpass. Here, we extend this work by analyzing all known bona fide
BALQSOs observed within the inner 20' of the ROSAT PSPC. This sample includes
both targeted and serendipitous exposures ranging from 8 to 75 ksec. Despite
these deep exposures, most of the BALQSOs are undetected, and have unusually
weak X-ray emission, as evidenced by large optical-to-X-ray slopes (AOX). Large
values of AOX ($\gapprox$1.8) may prove to be a defining characteristic of
BALQSOs. We predict that samples of QSO candidates with large AOX will yield a
higher percentage of BALQSOs, particularly at low redshift. As a corollary,
X-ray-selected QSO samples should yield The optical/UV emission line spectra of
BAL and non-BAL QSOs are quite similar, suggesting that their intrinsic
spectral energy distributions are similar as well. Absorption thus seems the
likely reason for the X-ray quiet nature of BALQSOs. To constrain the total
absorbing column of the BAL clouds, we compare our measured soft X-ray fluxes
or upper limits to those expected from normal radio quiet QSOs of comparable
optical continuum magnitude and redshift. From sensitive X-ray observations, we
derive column densities of greater than about 2 times 10^22 cm-2, for intrinsic
cold absorbers of solar metallicity. These new results suggest columns {\em at
least} an order of magnitude larger than the columns previously estimated from
optical/UV spectra alone.
