Context : Aims : We present a 0.2–200 keV broad-band study of absorbed AGN observed with INTEGRAL , XMM-Newton , Chandra and ASCA to investigate the continuum shape and the absorbing/reflecting medium properties . Methods : The sources are selected in the INTEGRAL AGN sample to have a 20–100 keV flux below 8 \times 10 ^ { -11 } erg cm ^ { -2 } s ^ { -1 } ( 5 mCrab ) , and are characterized by a 2–10 keV flux in the range ( 0.8–10 ) \times 10 ^ { -11 } erg cm ^ { -2 } s ^ { -1 } . The good statistics allow us a detailed study of the intrinsic and reflected continuum components . In particular , the analysis performed on the combined broad-band spectra allow us to investigate the presence of Compton reflection features and high energy cut-off in these objects . Results : The column density of the absorbing gas establishes the Compton thin nature for three sources in which a measure of the absorption was still missing . The Compton thin nature of all the sources in this small sample is also confirmed by the diagnostic ratios F _ { x } /F \left [ OIII \right ] . The Compton reflection components we measure , reflection continuum and iron line , are not immediately compatible with a scenario in which the absorbing and reflecting media are one and the same , i.e . the obscuring torus . A possible solution is that the absorption is more effective than reflection , e.g . under the hypothesis that the absorbing/reflecting medium is not uniform , like a clumpy torus , or that the source is observed through a torus with a very shallow opening angle . The high energy cut-off ( a lower limit in two cases ) is found in all sources of our sample and the range of values is in good agreement with that found in type 1 Seyfert galaxies . At lower energies there is clear evidence of a soft component ( reproduced with a thermal and/or scattering model ) , in six objects . Conclusions :