The current paradigm foresees that relativistic jets are launched as magnetically dominated flows, whose magnetic power is progressively converted to kinetic power of of the matter of the jet, until equipartition is reached. Therefore, at the end of the acceleration phase, the jet should still carry a substantial fraction ($\approx$ half) of its power in the form of a Poynting flux. It has been also argued that, in these conditions, the best candidate particle acceleration mechanism is efficient reconnection of magnetic field lines, for which it is predicted that magnetic field and accelerated relativistic electron energy densities are in equipartition.Through the modeling of the jet non--thermal emission, we explore if equipartition is indeed possible in BL Lac objects, i.e. low-power blazars with weak or absent broad emission lines. We find that one-zone models (for which only one region is involved in the production of the radiation we observe) the particle energy density is largely dominating (by 1-2 orders of magnitude) over the magnetic one. As a consequence, the jet kinetic power largely exceeds the magnetic power. Instead, if the jet is structured (i.e. made by a fast spine surrounded by a slower layer), the amplification of the IC emission due to the radiative interplay between the two components allows us to reproduce the emission in equipartition conditions.