Signal Detection models as well as the Two-High-Threshold model (2HTM) have been used successfully as measurement models in recognition tasks to disentangle memory performance and response biases. A popular method in recognition memory is to elicit confidence judgements about the presumed old/new status of an item, allowing for the easy construction of ROCs. Since the 2HTM assumes fewer latent memory states than response options are available in confidence ratings, the 2HTM has to be extended by a mapping function which models individual rating scale usage. Unpublished data from 2 experiments in Bröder and Schütz (2009) validate the core memory parameters of the model, and 3 new experiments show that the response mapping parameters are selectively affected by manipulations intended to affect rating scale use, and this is independent of overall old/new bias. Comparisons with SDT show that both models behave similarly, a case that highlights the notion that both modelling approaches can be valuable (and complementary) elements in a researcher's toolbox.