  We propose a charged, electrically neutral, and flavour changing Z' model to
conciliate the apparent disagreement between the important excess found in the
top-antitop Tevatron forward-backward asymmetry and the null -compatible with
negative- results found in the LHC charge asymmetry. We show that this model
contributes positively to the forward-backward asymmetry, whereas naturally a
new cancellation is turned on at the LHC, yielding a null, or even negative,
charge asymmetry. We found the region in parameter space that is simultaneously
allowed by the stringent Tevatron and LHC observables. We show that the model
is safe to atomic parity violation constraints and to tj resonance searches,
and propose a possible increase in the Z' width to avoid ttj constraints. We
evaluate the constraints to the model, as well as distinctive features in the
fore-coming experimental results.
