We study the pairing properties of the two-dimensional t -t'-t″-J model, where t' and t″ are second and third neighbor hoppings, at a doping level x ≈0.1 . Recent studies of the t -t'-J model find strong pairing for t'>0 , associated with electron doping, but an absence of pairing for t'<0 , associated with hole doping. This is in contrast to the cuprates, where the highest transition temperatures appear for hole doping. Model parametrizations for the cuprates estimate a t″ comparable to t', which, in principle, might fix this discrepancy. However, we find that it does not; we observe a suppression of pairing for the hole-doped system (t'<0 ,t″>0 ) , while for the electron-doped system (t'>0 ,t″<0 ) d -wave pairing is robust. Extended hoppings appear to be insufficient to make the one-band t -t'-J model capable of describing the pairing in the hole-doped system.