We present optical and X-ray data for a sample of serendipitous XMM-Newton sources that are selected to have 0.5-2 keV vs 2-4.5 keV X-ray hardness ratios which are harder than the X-ray background. The sources have 2-4.5 keV X-ray flux >= 10^-14 cgs, and in this paper we examine a subsample of 42 optically bright (r < 21) sources; this subsample is 100 per cent spectroscopically identified. All but one of the optical counterparts are extragalactic, and we argue that the single exception, a Galactic M star, is probably a coincidental association. The X-ray spectra are consistent with heavily absorbed power laws (21.8 < log NH < 23.4), and all of them appear to be absorbed AGN. The majority of the sources show only narrow emission lines in their optical spectra, implying that they are type-2 AGN. Only a small fraction of the sources (7/42) show broad optical emission lines, and all of these have NH < 10^23 cm^-2. This implies that ratios of X-ray absorption to optical/UV extinction equivalent to > 100 times the Galactic gas-to-dust ratio are rare in AGN absorbers (at most a few percent of the population), and may be restricted to broad absorption-line QSOs. Seven objects appear to have an additional soft X-ray component in addition to the heavily absorbed power law. We consider the implications of our results in the light of the AGN unified scheme. We find that the soft components in narrow-line objects are consistent with the unified scheme provided that > 4 per cent of broad-line AGN have ionised absorbers that attenuate their soft X-ray flux by >50 per cent. In at least one of the X-ray absorbed, broad-line AGN in our sample the X-ray spectrum requires an ionised absorber, consistent with this picture.
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