  Low-redshift active galactic nuclei (AGNs) with extremely blue optical
spectral indices are shown to have a mean, velocity-averaged, broad-line
H$\alpha$/H$\beta$ ratio of $\thickapprox 2.72 \pm 0.04$, consistent with a
Baker-Menzel Case B value. Comparison of a wide range of properties of the very
bluest AGNs with those of a luminosity-matched subset of the Dong et al. blue
AGN sample indicates that the only difference is the internal reddening.
Ultraviolet fluxes are brighter for the bluest AGNs by an amount consistent
with the flat AGN reddening curve of Gaskell et al.(2004). The lack of a
significant difference in the GALEX (FUV--NUV) colour index strongly rules out
a steep SMC-like reddening curve and also argues against an intrinsically
harder spectrum for the bluest AGNs. For very blue AGNs the Ly$\alpha$/H$\beta$
ratio is also consistent with being the Case B value. The Case B ratios provide
strong support for the self-shielded broad-line model of Gaskell, Klimek &
Nazarova. It is proposed that the greatly enhanced Ly$\alpha$/H$\beta$ ratio at
very high velocities is a consequence of continuum fluorescence in the Lyman
lines (Case C). Reddenings of AGNs mean that the far-UV luminosity is often
underestimated by up to an order of magnitude. This is a major factor causing
the discrepancies between measured accretion disc sizes and the predictions of
simple accretion disc theory. Dust covering fractions for most AGNs are lower
than has been estimated. The total mass in lower mass supermassive black holes
must be greater than hitherto estimated.
