The hemagglutination-inhibition (HI) assay is the main tool used by epidemiologists to quantify antigenic differences between circulating influenza virus strains, with the goal of selecting suitable vaccine strains. However, such quantitative measures of antigenic difference were recently shown to have poor predictive accuracy with respect to influenza vaccine effectiveness (VE) in healthy adults. Here, we re-examine those results using a more rigorous criterion for predictive accuracy -- considering only cases when the vaccine (V) and dominant (D) circulating strains are antigenically different -- and greater numbers of HI titers. We find that the Archetti -- Horsfall measure of antigenic difference, which is based on both the normalized HI titer (NHI) of D relative to antisera raised against V and the NHI of V relative to D, predicts VE very well (R(2)=0.62, p=4.1x10(-3)). In contrast, the predictive accuracies of the NHI of D relative to V alone (R(2)=0.01), and two other measures of antigenic difference based on the amino acid sequence of influenza virus hemagglutinin (R(2)=0.03 for both measures) are relatively poor. Furthermore, while VE in the elderly is generally high in cases when D and V are antigenically identical (VE=35%, S.E.=5%), in other cases VE appears to increase with the antigenic difference between D and V (R(2)=0.90, p=2.5x10(-5)). This paradoxical observation could reflect the confounding effects of prior immunity on estimates of VE in the elderly. Together, our results underscore the need for consistently accurate selection of suitable vaccine strains. We suggest directions for further studies aimed at improving vaccine-strain selection and present a large collection of HI titers that will be useful to such studies.