  We present the results of a detailed spectral analysis of optically faint
hard X-ray sources in the Chandra deep fields selected on the basis of their
high X-ray to optical flux ratio (X/O). The stacked spectra of high X/O sources
in both Chandra deep fields, fitted with a single power-law model, are much
harder than the spectrum of the X-ray background (XRB). The average slope is
also insensitive to the 2-8 keV flux, being approximately constant around
Gamma~1 over more than two decades, strongly indicating that high X/O sources
represent the most obscured component of the XRB. For about half of the sample,
a redshift estimate (in most of the cases a photometric redshift) is available
from the literature. Individual fits of a few of the brightest objects and of
stacked spectra in different redshift bins imply column densities in the range
10^{22-23.5} cm^{-2}. A trend of increasing absorption towards higher redshifts
is suggested.
