In recent years, the epistemic reliability of moral intuitions has been undermined by substantial empirical data reporting the influence of cognitive biases. This paper discusses and elaborates upon a promising strategy in response to the reliability challenge to moral intuitions. The considered argument appeals to the fact that moral intuitions are experienced with different levels of strength and agents accept only strong intuitions, not vulnerable to bias under realistic circumstances. This essay aims to reconstruct this defense from the reliability challenge (...) in its most promising form and to evaluate the plausibility of the argument in light of the available empirical evidence. What emerges from the discussion is that the vindication of moral intuitions fundamentally depends on two distinct premises: first, the hypothesis that agents accept moral intuitions proportionally to their level of confidence, and second, the hypothesis that intuitive confidence is epistemically reliable. While there is consistent evidence for the first hypothesis, there is still no conclusive evidence for the second. (shrink)