  We report the results from our analysis of a large set of archival data
acquired with the X-ray telescope (XRT) onboard Swift, covering the sky region
surrounding objects from the first Fermi Large Area Telescope (LAT) catalogue
of high-energy sources (1FHL), which still lack an association. Of the 23
regions analysed, ten did not show any evidence of X-ray emission, but 13 were
characterised by the presence of one or more objects emitting in the 0.3-10 keV
band. Only in a couple of cases is the X-ray counterpart located outside the
Fermi positional uncertainty, while in all other cases the associations found
are compatible with the high-energy error ellipses. All counterparts we found
have been studied in detail by means of a multi-waveband approach to evaluate
their nature or class; in most cases, we have been able to propose a likely or
possible association except for one Fermi source whose nature remains doubtful
at the moment. The majority of the likely associations are extragalactic in
nature, most probably blazars of the BL Lac type.
