One of the most influential applications of the concepts, methods and measures of social network analysis to the study of the social support transactions of older adults is the convoy model of social support. We draw on recent debates in network methodology to provide an assessment of the convoy model that explores the role of weak ties in the support networks of older adults. The social networks generated by the target diagram which operationalizes the convoy model display the structural and functional characteristics set out in its theoretical arguments. But not all of the ties constituting these networks are conduits of social support and, more importantly, these social networks do not include all supporting and supported others. The target diagram identifies core support networks; therefore, support flowing through weak ties is missed when it is used to set the boundaries of support networks. Expanding our picture of the support networks of older adults to take systematic account of weak ties and the emotional aid, instrumental assistance, and companionship that flow through them will enhance the effectiveness of support interventions that target older adults.