We have found that 4 new, bright IRAS quasars, out of 7 observed, have strong, non-variable, wavelength-dependent polarization. Three show degrees of polarization, pλ, increasing from infrared to UV wavelengths (Fig. 1), which implies a combination of a polarized, scattered spectrum and a much redder, unpolarized spectrum. Detailed IR and optical polarimetry and spectrophotometry of one, IRAS 13349+2438 (Wills et al.), shows a polarized flux spectrum, pλxFλ, (continuum and Pa α, Hα, and Hβ broad hydrogen lines) typical of unreddened, luminous quasars. This suggests that the path of scattered light from a central, luminous quasar is low in dust and that the polarization of the scattered spectrum is wavelength independent. The latter is most easily explained by electron scattering although the data do not exclude dust scattering. When this polarized flux spectrum is subtracted from the total spectrum, we are left with a very reddened line and continuum spectrum, E(B-V) = 0.3 to 0.7, which we attribute to the same luminous quasar seen through a thick dusty torus. The angle of polarization is parallel to the major axis of the r-band image, presumed to be that of the host galaxy. If the torus is in the plane of the galaxy, the axial ratio suggests a viewing angle of 40° to the plane of the torus. Fig. 2 illustrates the geometry. The appearance of the quasar at optical and UV wavelengths will depend strongly on viewing angle, suggesting that present samples of quasars selected by colours, optical flux density, or quasi-stellar appearance, may be seriously biased, with important consequences for studies of the space density and evolution of AGN.