  The convex (concave upward) high-energy X-ray spectra of the blazar
PKS\,2155-304, observed by \emph{XMM-Newton}, is interpreted as the signature
of sub-dominant 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 cutoff $\gamma_{\rm min}m_{\rm e} c^2$ of the radiating electron
distribution and the kinetic power $P_{\rm j}$ of the jet. We deduce these
quantities through a statistical fitting of the broadband 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 $\gamma_{\rm min} \gtrsim 60$, with a
preference for a value around $\gamma_{\rm min} \simeq 330$. The required
kinetic jet power is of the order of $P_{\rm j} \sim 3\times 10^{45}$ 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 fit parameters support the X-ray emitting part of
blazar jets to be dominated by an electron-proton rather than an
electron-positron composition.
