  We have performed a successful targetted search for a population of red
radio-quiet, and probably absorbed, quasars. Radio-quiet, optically-red ROSAT
PSPC X-ray sources brighter than 10^{-13} erg cm^{-2} s^{-1} were searched for
red (O-E > 2.0, O < 20) counterparts in the APM catalog of Palomar Sky Survey
objects. Of 45 objects for which we obtained adequate follow-up optical
spectroscopy, we have found 7 red quasars, 5 with alpha(opt) < -2. Their
redshifts range from 0.06 to 0.31, and their luminosities are moderate, lying
on the Seyfert/Quasar boundary. These red quasars strengthen the case for a
radio-quiet population that is the counterpart of the radio-loud red quasars
found by Smith and Spinrad (1980), and Webster et al. (1995). Unidentified,
fainter, sources could increase the fraction of red quasars by up to a factor
7.
  For the red quasars found here, the H-alpha/H-beta ratios, optical slope and
X-ray colors all indicate that they are absorbed by A(V) ~ 2, rather than
having intrinsically red spectra. This amount of obscuration seems to hide
~1-7% of quasars at a given observed flux, or ~3-20% when their fluxes are
corrected to their intrinsic values. This size of population is consistent with
earlier limits, with predicted values from Comastri et al. (1995), and is
comparable to the rate found among radio-loud quasars.
  A large population of more heavily absorbed (A(V)=5), fainter, quasars equal
in size to the blue population could exist, without violating existing upper
limits, in accord with the Comastri et al. (1995) predictions.
