Past research has indicated that a person's speed on cognitive tasks is correlated with his or her intelligence (Sheppard & Vernon, 2007). This has influenced the belief that faster respondents on intelligence tests may be more intelligent than those who are slower. Within this context, previous research has employed a one-parameter item response tree model to intelligence test data and concluded that there are two unique test-taking processes: one process for fast responses, and one for slow responses (Partchev & De Boeck, 2012). This study asks similar questions, but instead uses a two-parameter item response tree model. This model allows the researcher to calculate separate sets of item parameters for when an item is answered quickly versus when it is answered slowly. This item response tree model is fit to 503 respondents to a matrix intelligence test and 726 respondents to a verbal test. Results show that each item has separate parameters for fast and slow responses. Furthermore, for both matrix and verbal tests, the item discrimination parameters are consistently higher for fast responses, suggesting that fast responses to an item may contain more information about the ability of the respondent than slow responses.