Social media is increasingly being used to support interaction among family members. However, differences in media preferences and interaction patterns challenge intergenerational communication. It impacts negatively on the physical and mental health of older adults. Trying to bridge such a communication asymmetry, this paper reports the primary results of an analysis conducted on an existent dataset from two 21-weeks deployment studies, along with a 3-week design study, to understand intergenerational communication mismatches among older adults and relatives. Results indicate opportunities that informed the design and implementation of the Social Connector system, a software application that allows older adults to establish synchronous and asynchronous social interactions with their relatives. The paper also describes this system and discusses the main design decisions made to try reducing the stated communication asymmetry.