Recently, the issue of the role of the Eddington limit in accretion discs became a matter of debate. While the classical (spherical) Eddington limit is certainly an over-simplification, it is not really clear how to treat it in a flattened structure like an accretion disc. We calculate the critical accretion rates and resulting disc luminosities for various disc models corresponding to the classical Eddington limit by equating the attractive and repulsive forces locally. We also discuss the observational appearance of such highly accreting systems by analyzing their spectral energy distributions. Our calculations indicate that the allowed mass accretion rates differ considerably from what one expects by applying the Eddington limit in its classical form, while the luminosities only weakly exceed their classical equivalent. Depending on the orientation of the disc relative to the observer, mild relativistic beaming turns out to have an important influence on the disc spectra. Thus, possible super-Eddington accretion, combined with mild relativistic beaming, supports the idea that ultraluminous X-ray sources host stellar mass black holes and accounts partially for the observed high temperatures of these objects. © 2007 International Astronomical Union.