When is manipulation all about the ones and twos?*

A mechanism is pairwise strategy-proof if groups of size one and two never have an incentive to manipulate. When agents have strict preferences over their own outcomes, I show that pairwise strategy-proofness even eliminates incentives for any group of agents to manipulate, therefore implying group strategy-proofness. It is also equivalent to Maskin monotonicity. I obtain the equivalence results assuming preference domains satisfy a richness condition. Decomposing richness into two parts, I explore what brings about the equivalence. The results apply to school choice and matching with contracts, indivisible object allocation, and economies with private or public goods with single-peaked preferences. JEL Classification: C78, D71, D82