We measure entropy production as a functional over trajectories in a Markovian steady state: this has usually the meaning of energy dissipated by the external driving force and (if this force is constant) is proportional to the current generated by the force. Our question is: how this entropy production (its average and fluctuations) change when a set of "fast" states is removed from phase space through some decimation procedure? Some arguments, supported by numerical simulations, suggest that the decimation leaves entropy production almost unchanged. The situation changes if entire "loops" are removed by decimation, an event which does not seem to be generic.