The t − J model is a standard model of strongly correlated electrons, often studied in the context of high-T_c superconductivity. However, most studies of this model neglect three-site terms, which appear at the same order as the superexchange J. As these terms correspond to pair hopping, they are expected to play an important role in the physics of superconductivity when doped sufficiently far from half filling. We present a density matrix renormalization-group study of the one-dimensional t − J model with the pair hopping terms included. We demonstrate that these additional terms radically change the one-dimensional ground-state phase diagram, extending the superconducting region at low fillings, while at larger fillings, superconductivity is completely suppressed. We explain this effect by introducing a simplified effective model of repulsive hardcore bosons.