The current problem in building a conversational model from Twitter data is the scarcity of long conversations. According to our statistics, more than 90% of conversations in Twitter are composed of just two tweets. Previous work has utilized only conversations lasting longer than three tweets for dialogue modeling so that more than a single interaction can be successfully modeled. This paper verifies, by experiment, that two-tweet exchanges alone can lead to conversational models that are comparable to those made from longer-tweet conversations. This finding leverages the value of Twitter as a dialogue corpus and opens the possibility of better conversational modeling using Twitter data.