The Response Time-Based Concealed Information Test (RT-CIT) can reveal when a person recognizes a relevant ("probe") item among other, irrelevant items, based on comparatively slow responses to the probe item. For example, if a person is concealing his or her true identity, one can use the suspected identity details as probes, and other, random details as irrelevants. However, in our study, we show that even when participants are merely informed about such probes (i.e., the relevant identity details) before performing the RT-CIT, their responses will also be slower to these details. Hence, it is more difficult to distinguish such innocent but pre-informed persons from actually guilty persons. At the same time, we introduce a CIT version with familiarity-related inducer stimuli, but with no targets, that elicits probe-minus-irrelevant RT differences only among guilty participants but not among informed innocent participants. Implications for the theory and the application of CITs are discussed.