When allocating resources, people often have to resolve a conflict between equity and efficiency concerns. That is, sometimes for everyone to receive the same amount of resources, some resources must be used suboptimally. However, it is unclear whether and how people account for the impact their allocation decisions would have on the recipients' outcome. In three experiments, we examine how the amount of resources allocated to the recipients influences allocators' decisions and use mouse tracking techniques to assess their conflict during the decision process. The results reveal that when an equitable allocation of resources led to neither recipients receiving anything nor imposed losses, people tended to prefer efficient allocations. Such allocations between recipients who may end up with no resources also evoke a greater conflict compared with allocations in which both recipients have some secured gains, suggesting that, in general, people want to be equitable but not when equity means that nobody gets anything. When maintaining equity can only be done by leaving recipients with no resources at all, equitable allocations evoke a greater conflict, and people are more likely to refrain from them.