The rapidly declining population of bright quasars at z 3 appears to make an increasingly smaller contribution to the ionising background at the H I Lyman limit. It is thererfore generally thought that massive stars in (pre-)Galactic systems may provide the additional ionising flux needed to complete H I reionisation by z 6. A galaxy-dominated background, however, may require that the escape fraction of Lyman continuum radiation from high-redshift galaxies is as high as 10%, which is somewhat at odds with (admittedly scarce) observational constraints. High escape fractions from dwarf galaxies have been advocated, or, alternatively, a so-far undetected (or barely detected) population of unobscured, high-redshift faint AGNs. Here we examine the latter hypothesis and show that such sources, to be consistent with the measured level of the unresolved X-ray background at z = 0, can provide a fraction of the H II filling factor no larger than 13% by z 6. The fraction rises to 27% in the somewhat extreme case of a constant comoving redshift evolution of the AGN emissivity. This still calls for a mean escape fraction of ionising photons from high-z galaxies of 10%.