An old issue in psychological assessment is to what extent power and speed each are measured by a given intelligence test. Starting from accuracy and response time data, an approach based on posterior time limits (cut-offs of recorded response time) leads to three kinds of recoded data: time data (whether or not the response precedes the cut-off), time-accuracy data (whether or not a response is correct and precedes the cut-off), and accuracy data (as time-accuracy data, but coded as missing when not preceding the time cut-off). Each type of data can be modeled as binary responses. Speed and power are investigated through the effect of posterior time limits on two main aspects: (a) the latent variable that is measured: whether it is more power-related or more speed-related; (b) how well the latent variable (of whatever kind) is measured through the item(s). As empirical data, we use responses and response times for a verbal analogies test. The main findings are that, independent of the posterior time limit, basically the same latent speed trait was measured through the time data, and basically the same latent power trait was measured through the accuracy data, while for the time-accuracy data the nature of the latent trait moved from power to speed when the posterior time limit was reduced. It was also found that a reduction of the posterior time limit had no negative effect on the reliability of the latent trait measures (of whatever kind).