Being able to successfully engage in conversation is an important skill for most adults. When an adult has aphasia, this skill is affected. Traditionally, speech-language pathologists try to increase language skills in people with aphasia in an effort to ultimately improve performance in functional activities such as conversation. However, conversation is a complex communication task that places demands not only on linguistic processing, but also on higher level cognitive processing. In this paper, we describe our initial efforts to improve conversational success in people with aphasia when training their attention on simple non-linguistic computer tasks.