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tokens: index Γ and the inner disc temperature are consistent with the results of previous studies of M33 X-8, where a similar spectral model and data from Swift /XRT (La Parola et al. 2015 ), XMM–Newton (Foschini et al. 2004 ), or Suzaku (Isobe et al. 2012 ) were used. The innermost disc radius, R in , can be directly estimated from the normalization of the diskbb component: , where D is the distance to the source in units of 10 kpc and i is the inclination of the disc. The estimated inner disc radius, R in = (37 ± 2)cos −1/2 i km, is in good agreement with the results of previous studies (e.g. Middleton et al. 2011 ). Associating this size with the radius of the innermost stable orbit of a standard accretion disc suggests that the relativistic compact object has a mass of at least ∼4 M ⊙ , with the exact value depending on the (unknown) inclination of the disc. More accurate estimation should take into account the inner boundary condition, the spectral hardening and relativistic corrections, which in turn would depend on the structure of the accretion disc (whether it is thin or slim). Nevertheless, the above crude estimate is consistent with the compact object being a stellar-mass black hole. Replacing the power-law component by its modification with an exponential cut-off (Model 5) further improves the fit statistics to χ 2 /d.o.f. =891/900, indicating the presence of a high-energy cut-off in the spectrum (the F -test probability is 10 −14 for the null-hypothesis Model 4). We conclude that the broad-band 0.3–20 keV spectrum of M33 X-8 cannot be described by a single accretion disc model diskpbb , which was previously used to successfully fit some narrow-band spectra of this source (e.g. La Parola et al. 2015 ). The broad-band spectrum strongly requires an additional power-law component with a possible high-energy cut-off. 3.3 Physically motivated models We have demonstrated that the broad-band spectrum of M33 X-8 certainly contains two components: the first one is well approximated by a multicolour disc with the inner temperature of kT ∼ 1 keV, and the second one is a power-law-like high-energy tail detected up to 20 keV. As often discussed in the literature (e.g. Gierliński et al. 1999 ; Steiner et al. 2009 ), the combination of a low-energy blackbody-like component with a high-energy power law does not allow one to properly model the spectrum at low energies, because a steep power law extending to the soft part of the spectrum requires the introduction of an artificially high absorption column density and can result in erroneous determination of the disc properties. This problem can be solved by using a self-consistent Comptonization model that has a low-energy cut-off in the otherwise power-law-like spectrum, such as the convolution model simpl (Steiner et al. 2009 ), which provides a description of Comptonization based on the non-relativistic theory developed by Sunyaev Titarchuk ( 1980 ). In this model, a fraction of the photons from an