Response bias (or criterion) contamination is insidious in studies of consciousness: that observers report they do not see a stimulus may not mean they have absolutely no subjective experience; they may be giving such reports in relative terms in the context of other stimuli. Bias-free signal detection theoretic measures provide an excellent method for avoiding response bias confounds, and many researchers correctly adopt this approach. However, here we discuss how a fixation on avoiding criterion effects can also be misleading and detrimental to fruitful inquiry. In a recent paper, Balsdon and Azzopardi (Absolute and relative blindsight. Consciousness and Cognition 2015; 32:79–91.) claimed that contamination by response bias led to flawed findings in a previous report of “relative blindsight”. We argue that their criticisms are unfounded. They mistakenly assumed that others were trying (and failing) to apply their preferred methods to remove bias, when there was no such intention. They also dismissed meaningful findings because of their dependence on criterion, but such dismissal is problematic: many real effects necessarily depend on criterion. Unfortunately, these issues are technically tedious, and we discuss how they may have confused others to misapply psychophysical metrics and to draw questionable conclusions about the nature of TMS (transcranial magnetic stimulation)-induced blindsight. We conclude by discussing the conceptual importance of criterion effects in studies of conscious awareness: we need to treat them carefully, but not to avoid them without thinking.