We use a recent upper limit from CDF on like-sign top pair production to place constraints on general new vector bosons and scalars mediating u u -> t t. The possible vector bosons comprise neutral colour singlets or octets, and charge 4/3 colour triplets or sextets, whereas the new scalars can be neutral colour singlets or octets and charge 4/3 colour sextets. We also estimate the expected bounds from like-sign top pair production at LHC in the near future. Then, we address the implications of

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... these limits for the forward-backward asymmetry in t tbar production measured at Tevatron. In particular, we find that models explaining the observed asymmetry by the exchange of a single t-channel heavy Z' boson are already excluded. On the other hand, light Z' bosons with a mass M_Z' ~ 150 GeV, which could also account for a recent CDF dijet excess in W+jet production, are barely allowed.