The essay reports two studies on confirmatory factor analysis of speeded data with an effect of selective responding. This response strategy leads test takers to choose their own working order instead of completing the items along with the given order. Methods for detecting speededness despite such a deviation from the given order are proposed and investigated. The first study demonstrated that speededness was not detectable if the deviation was large and selected by all test takers but ignored in investigating the data. Adaptation to the selected working order restored the detectability. The second study assumed four groups of test takers selecting group-specific working orders. Detection of speededness required a confirmatory factor model with speed factors adapted to group-specific working orders.