It is generally assumed that amino acid mutations in the surface protein, hemagglutinin (HA), of influenza viruses allow these viruses to circumvent neutralization by antibodies induced during infection. However, empirical data on circulating influenza viruses show that certain amino acid changes to HA actually increase the efficiency of neutralization of the mutated virus by antibodies raised against the parent virus. Here, we suggest that this surprising increase in neutralization efficiency after HA mutation could reflect steric interference between antibodies. Specifically, if there is a steric competition for binding to HA by antibodies with different neutralization efficiencies, then a mutation that reduces the binding of antibodies with low neutralization efficiencies could increase overall viral neutralization. We use a mathematical model of virus-antibody interaction to elucidate the conditions under which amino acid mutations to HA could lead to an increase in viral neutralization. Using insights gained from the model, together with genetic and structural data, we predict that amino acid mutations to epitopes C and E of the HA of influenza A/H3N2 viruses could lead on average to an increase in the neutralization of the mutated viruses. We present data supporting this prediction and discuss the implications for the design of more effective vaccines against influenza viruses and other pathogens.