ABSTRACT The convex (concave upward) high-energy X-ray spectra of the blazar PKS 2155-304, observed by XMM-Newton, is interpreted as the signature of subdominant inverse-Compton emission. The spectra can be well fitted by a superposition of two power-law contributions which imitate the emission due to synchrotron and inverse-Compton processes. The methodology adopted enables us to constrain the photon energy down to a level where inverse-Compton emission begins to contribute. We show that this information supplemented with knowledge of the jet Doppler factor and magnetic field strength can be used to constrain the low-energy cut-off γminmec2 of the radiating electron distribution and the kinetic power Pj of the jet. We deduce these quantities through a statistical fitting of the broad-band spectral energy distribution of PKS 2155-304 assuming synchrotron and synchrotron self-Compton emission mechanisms. Our results favour a minimum Lorentz factor for the non-thermal electron distribution of γmin ≳ 60, with a preference for a value around γmin ≃ 330. The required kinetic jet power is of the order of Pj ∼ 3 × 1045 erg s−1 in case of a heavy, electron–proton dominated jet, and could be up to an order of magnitude less in case of a light, electron–positron dominated jet. When put in context, our best-fitting parameters support the X-ray emitting part of blazar jets to be dominated by an electron–proton rather than an electron–positron composition.