In an attempt to simplify data analysis and to avoid confounds due to speed-accuracy trade-off, sometimes integrated measures of speed and accuracy are used. Although it has been claimed that some of these combined measures are insensitive to speed-accuracy trade-off (SAT), a systematic and broad examination of such claims has not been performed thus far. The present article reports the results of four simulation studies in which five established integrated measures were studied in different speed-accuracy trade-off contexts. All four studies used repeated measures designs crossing an experimental factor (variable of interest) with a factor representing SAT settings, with all conditions occurring randomly over the sequence of trials to avoid condition-wise SATs (mixed conditions repeated measures design). The first study used speed modulations that were balanced by accuracy changes in the opposite direction. The other studies were all based on SAT as modeled either by the drift-diffusion model, with pro-active trade-off settings (Study 2) or with reactive trade-off modulations (Study 3) or by a discontinuous two-phase model (Study 4). Only the studies based on balanced trade-offs showed that two of the measures were insensitive to SAT settings, while in all other contexts, all measures were sensitive to SAT. Nevertheless, as the mixed conditions design distributes the SAT effects over the conditions of the variable of interest, all integrated measures reliably detected the effect of this variable in all SAT conditions. Although integrated measures are sensitive to SAT, these effects can be neutralised by using a mixed conditions repeated measures design.